I do agree that a snowflake is not a religious item. I do not celebrate the religious aspects of holidays, but I do engage in the secular ones. I give and get gifts, cards, et cetera. I even have my car decorated in snowflakes - not for Christmas, but for winter! Just because it has a string that enables it to be hung does not mean it must be a Christmas ornament to hang on a tree. Hang it from a suction cup and put it on your bedroom window, bathroom mirror, etc. Hang it from a nail like you would a painting. It's an "ornament" only in that it is a decoration, an adornment (that's where the "orn" comes from in ornament I guess). The accompanying note was not offensive in the least. The only way I can think of that it could be interpreted as a Christmas gift was the timing of when it was handed out, and that relies on assumptions by the parents, which they've demonstrated in their little missive to the OP.
Regarding gifts in the classroom, I do generally think they should not have religious connotations in the gift ITEM itself, but the occasion may very well have something to do with it. Christmas, Hanukkah, et cetera. My local school permits gift exchanges and birthday invites, but they do say that you must either give to ALL the kids in the class, or give them outside of the classroom (i.e. at the end of the day when you're outside getting on the bus to go home, or away from school entirely) to avoid favoritism/bullying situations. Funnily enough, during Christmas, we generally made decorations for the classroom and just had a party day - bringing in cupcakes, cookies, etc - rather than exchanging presents. Those who were meant to get presents got them outside of school anyway. (Best friends and so on) Same for Valentine's Day. Other holidays, like Easter, Hanukkah, and so forth were acknowledged with some in-class activities rather than presents. I remember one year when all events were food oriented. Latkes for Hanukkah for example. We researched recipes and the history of those foods and things like that.
Those parents need to learn that they are not going to shelter their child forever. As parents they can certainly say "we don't give/get gifts unless they are religious-themed" but they need to take ownership of their actions too, rather than blaming someone who does not know these personal rules they've established for their family. In the future, OP, I would check with the school to see what the policy is. If the policy is "universal or none" then continue to give nonspecific items to your child's class, including this child, as long as your child wishes to do so. There's no reason she should be denied the pleasure of giving to people she likes just because ONE child's parents object. If there is no universal policy, then you might sit down with your daughter and explain that you've discovered that the child's parents don't want to get gifts during common holidays because of their religious beliefs. Then quietly instruct your daughter to not give this child a gift, but to instead personally interact with them. Go over and give them a hug if they are that friendly, talk about how you hope they'll have a great day, things like that. This way the child might not feel quite so left out. (If the child says 'but you didn't give me anything and gave them things,' your daughter might say, 'your parents told mine that it wasn't appropriate to give you anything. Did we misunderstand?') I forget how old these kids are... eventually that kid will grow up and adopt his own policy regarding that. If he wants to adhere to the example his parents set, great!
Regarding religious holidays... Many now have secular aspects as well as religious ones. Is it right to universally ban all holidays because they MIGHT be religious? That's not really something we can discuss on this forum, but it's something to consider.