Great car. Mine has almost 200K, my daughter's is going on 180K. Having had several Fits of the first two generations, I can attest that they handle just fine in snow- PROVIDING YOU INSTALL 4 SNOW TIRES for winter driving. Bridgestone, Michelin, Continental, Nokia are all good for snow and ice service. Do NOT count on reliable winter traction in any car with All Season tires. They are mis-named, and are truly only good for 3 season- not Winter. However, the new type of "ALL WEATHER" TIRES are reputed to be close to snow tires in winter traction, and might bbe worth trying. Nokia WRG3 and Toyo CELSIUS are the two that have been around the longest. I might try one of them on my next round of winter tire purchases.
Since the ground clearance is not that great, deep snow that the car rides up over will not be easily driven through, and you should not expect to pass through, without getting stuck. Always keep a shovel with you, and a winter emergency kit, however.