Skimming cookbooks, visiting new-to-you grocers, and sampling cuisines can be fun forms of research. Just remember to be respectful when entering someone else's space. Feel free to ask questions, but don't expect people to disregard regular customers or business to indulge your curiosity or hold your hand. For all they know, you're a one-time gawker.
The Mexican food I associate with winter, and Christmas more specifically, is tamales. I vividly remember the one Christmas our family made tamales from scratch. It was women's work and there was much laughter and gossip and excitement at passing down the tradition. There was also a lot of muscle power involved, as my rail-thin great-aunt cranked the meat grinder to make the filling. I suspect one reason tamales are a holiday food is precisely because it can take a village. There's so much work, it's more fun as an assembly line. Also, with all the people in the kitchen and the steaming going on, it gets really warm, even in a poorly insulated house in the middle of winter. Tamales can be sweet or savory, but I never had sweet until I moved away from home. It just wasn't something we did, and I don't know if that was cultural or family-specific. I like this recipe/historiography about tamales.
My husband reminisces about Las Posadas at his aunt's house. In her community, folks would recreate the procession of Mary and Joseph in search of shelter for the night. At each home, the occupants would turn "Mary and Joseph" away, then join the procession until the entire neighborhood showed up at the aunt's house, where they were all welcomed and a celebration ensued. Obviously, the event took days of preparation, and part of that preparation was the slaughtering of a pig. My husband says that this was also very gender-divided work, with the boys and men expected to stay outside and do (or watch) the killing and the females inside doing the cooking. My husband hated that tradition.
The gendered roles in traditional cooking can be quite problematic, with their normative assumptions about what a man or woman should do/like/be. Alberto Yáñez's short story "Recognizing Gabe" acknowledges how difficult such divisions can be for transgender people, in particular.
Something my husband and I can hate in common is menudo. Since it's a hot soup, it's generally a winter time food. I remember families going home from high-school football games (VERY big in South Texas) and delighting in the prospect of warming up with the menudo waiting for them at home. J and I are not fans of eating organs in general, and there's a distinct smell to tripe that neither of us can get past.
Something that's much easier to love is Mexican hot chocolate, which has more spice (cinnamon) to it than regular hot cocoa. We grew up with the Abuelita brand.
Even if your story does not involve a holiday, food details can enrich the characters and setting. For example, our household eats a lot of Mexican food. It's our comfort food. When I'm feeling sad, I often want beans and rice and enchiladas. (If we go out to eat and I'm feeling fragile, chances are I'll choose the neighborhood Mexican place, because no one will look at me "that way.") Our family's too-tired-to-think go-to meals are Mexican or Mexican-inspired: chilaquiles, burritos, tacos, nachos, quesadillas, black bean and tofu scramble. Our special treats include black bean soup, maranitos, sweet empanadas, botanas, and tamales. And meals that wouldn't ordinarily be considered Mexican become so in our household, because we use cumin, garlic, onion, and chili powder the way other families use oregano and basil or fennel and marjoram.
Contrary to most fast-food versions of Mexican food, our homemade food is not smothered in cheese or sour cream. Using ALL THE CHEESE is not authentic. Besides, my daughter and I are lactose sensitive (as is most of my side of the family). It's unclear how prevalent lactose intolerance is among Latin@s. At least 10% of Latin@s self-report as lactose intolerant, whereas some studies predict 50-80% are lactose intolerant. In any case, I make our cocoa with soy milk.
Of course, my extended family might argue that some of my food doesn't "count" as Mexican. When my aunt found out we intended to raise our daughter vegetarian (we didn't, but that's another story), supposedly she said, "But then she'll never taste fajitas!" Apparently mushroom and veggie fajitas don't count? Likewise, TVP burritos, soy-rizo, and Quorn tacos would be oh-so-wrong. This kind of conflict can be useful for storytelling. Cooking disputes can reflect conflicting values, or generational differences. Your Latin@ character might roll their eyes at someone else's food choices, or they might welcome the variety at a potluck or family function.
You can convey a lot about a character by showing how they react to new foods. For example, I became much more interested in trying different cuisines when I realized most cultures have a tortilla correlate or proxy. There's fry bread and pita and na'an and the pancakes in mu shu pancakes and crepes. However similar to or different from those foods tortillas actually are, that's what I compare them to, because that's what I know. Likewise, when I encounter a pupusa, I think it's like a gordita, whereas someone else might think, oh a pasty! So get inside your Latin@ character's head and figure out what their foods are and what they're going to be comparing everything else to.
On the other hand, just as some people are "meat and potato" folks, with no interest in experimenting, some people are "rice and beans" folks and anything outside their traditional meals is viewed with suspicion or dread. And, of course, just because your character is Latin@ doesn't mean they can or want to cook (or eat) traditional foods—they might be into South Indian cuisine or really love sushi or crave wasabi peas. If they hate okra, they probably hate nopales, too, because both can get slimy if not prepared properly.
Other matters to consider regarding your Latin@ character and their relationship to food.
Latin@s are not immune to eating disorders. (see also) Research has shown that Latinas have higher rates of binge eating than other groups. Adolescent Latinas, in particular, may have the highest rates of dieting and unhealthy weight control behaviors. (The trend seems to be that the more assimilated one gets, the greater the likelihood of having an eating disorder.) And yet, I can't think of one story I've read in which the person with an eating disorder was Latina.
If allergies and sensitivities are underdiagnosed among the general population, they are usually even more so among minority populations, who are understudied and for whom traditional diagnostic rubrics may not work. I already mentioned the uncertainty regarding lactose sensitivity in Latin@ populations. The incidence of celiac disease among black, Latin@, and Asian Americans is estimated to be 1 in 236. But there doesn't seem to be enough research among the individual minority groups, so take that stat with a salt lick.
About 12% of Latin@s have diabetes, which is a rate 66% higher than the non-Hispanic white population. Among the Latin@ population, the incidence rates seem to be highest for Mexican-Americans and Puerto Ricans. Adjusting to a new diet is hard even when you have plenty of resources and support, but imagine what it's like for recent immigrants, who may not be able to find or afford products that are both healthy and nurturing in their familiarity.
Add these food realities to whatever SFnal premise your characters face, and those characters become more complicated, three-dimensional. A great example is Gordo, in Daniel José Older's "Salsa Nocturna", who takes his high-blood pressure medication every morning with a side of bacon or sausage, for balance. If I hadn't loved Gordo from paragraph one, then this admission of his in paragraph two would've completely won me over.