Hi!
Here are 2 Non religious Winter party crafts I have done in the past as a room mom for holiday parties:
TUBESOCK SNOWMAN:
1. Tubesock snowman

urchase kids tubesocks. Each child gets a sock and fills it with a little zip bag of rice at the bottom for weight, then stuff with some polyfill about 2/3rds full and then knot or rubberband top of sock(leaving enough room to turn sock over inside-out to make a snowman ski cap like hat and glue a pom pom on top of closure to complete cap, for younger kids I used googly eyes, then cut sticky back felt into shapes for nose, mouth, etc... for older kids they can get small 'jingle bells' with a piece of wire threaded in sock and then 'twist tie' onto snowman, to make a neck I usually get some felt or plaid non fraying fabric and cut into a 'scarf' length with fringe, that the child can tye around to make the body/head of snowman. See link below with a variation of this craft to get the idea!
http://www.imagitek.com/xmas/crafts/sock_snowman.html
(FYI: For every school craft activity I always Pre-make my own 'kits' for each child in zip bags, this makes it easier to pass the craft around and make sure everyone has all the needed pieces to make the craft - labels with their name then when they complete the craft the item goes into the labeled bag to go home)
SNOWMAN SNOW MEASUREMENT STICK:
2. If you live in an area where there is measurable snowfall amounts you can either get free wooden paint stirrers (at big box home improvement stores) and mark off with a sharpie pen the incremental lines for the 1/2 inch and whole inches (have children draw each number 1 -12) or purchase a ready made ruler at the dollar store. Then glue on a flat wooden snowman on top (if you are under a time constraint for the party you can use acrylic paint and pre-paint snowman white and hot glue snowman (precut wooden flat snowman from craft store) at home or in class, then have child decorate with either crayons, markers, with googly eyes and/or felt embelishments. You can also write a phrase 'such as 'let it snow' on the ruler.
Remember you can take any of these ideas and modify them to fit your budget, age, and time!
Good Luck!