Typically, we say "on Christmas day" or "on Christmas eve". "on Christmas" feels like I am missing something. If Christmas is on the weekend, I could say "on Christmas weekend". "at Christmas" also feels incomplete. I would say "at Christmas dinner", "at Christmas mass", "at the Christmas party" or other event, such as plays or concerts, etc. I think that "on" is best used with some notion of time and "at" with some notion of place or event that occurs in a known type of location that you can picture in your mind. Yet, I believe some people use "on" or "at" and you just assume from the context whether they mean Christmas time or Christmas day and whether they mean at home or somewhere else. For this sentence "What are you doing for Christmas?" is really the best way to say it. You could be anywhere and it is an unknown length of time. For instance, I could be going to visit family for Christmas and I may be there for a week or more. There could be several events I am going to.
I marked "What are you doing for Christmas?" only and was told I am wrong for not marking "What are you doing during Christmas?" as a correct answer as well. How does "en" mean "during" ?!!! I don't see any "durante" in the sentence!
Also, wouldn't "What are you doing on Christmas?" which is not shown as an option be a better translation than saying "for Christmas"?
You're better off looking it up yourself instead of hoping a Spanish expert sees requests!
It's also worth looking up 'food' and seeing what verbs go with it, like in the Compound Forms bit lower down:
(looks like hacer is fine but preparar might be more common. Hacer la comida is listed here too, #9: http://lema.rae.es/drae/srv/search?val=hacer )
Hacer means 'make' (among other things) which is why you can use it when you're talking about 'making food', but you need the concept of food in there somewhere, otherwise it's just making... what?
So the sentence could be 'what are you making at Christmas' (maybe, I'm not 100% on the en working for both translations) and you could interpret that as 'what are you cooking', but that's not what it says. It's ambiguous, the speaker could have meant making handmade gifts, for example. If you translate it as 'cooking', you've made the sentence specifically about food, which the original wasn't, so you've changed the meaning - and it could be what the speaker meant, or it might not, but you don't know. Know what I mean?
You just need to be careful about accurate translations that don't add or remove too much information. It can be tricky, and you can't avoid it sometimes (like how está could be him, her or it, or usted, and you have to go with one) but it's the safest way to get through Duo