They hold up just fine; I've had mine for several years now, it stays outside all the time, and I've never had a problem. If it's a particularly wet and heavy snow, I'll go out and brush the snow off once it builds up - just to be safe.
But, be careful of smacking your windows too hard when they are cold, since they are more brittle and prone to breaking.
My TJ soft top holds up just fine and we had a pretty harsh winter last year. The only trouble is the wet heavy stuff will tend to freeze/bond with the top so you can't get it all off... and then later when you are going down the highway and it starts to "unstick", huge chunks will go flying and could hit other cars.
But that just makes it fun!
I'm curious how my huge JK 4-door softop will hold up.
2007 Wrangler Sahara Unlimited 4-door, Silver, 4.10, Teraflex 2.5" BB, 33x12.5x18 Toyo Open Country MT, 2" spacers, Sony video, Trail Guide GPS, TV tuner, MOPAR remote start
1998 Wrangler Sahara - built for fun - SOLD
Look at where the Jeeps are designed, built and tested. Michigan/Ohio. Not exactly your sun belt.
We have plenty of JK's around here that spend all winter with the softtops in whatever Michigan can send it's way. The tops survive just fine.
'00 TJ With toys, lift and tires.
'10 Dodge Ram 1500 Quad 4x4. Daily driver and tow rig
'05 Dodge Neon. Wifes daily driver and gas sipper.
There is no Bandaid for Stupidity
Sorry if my support of legal wheeling offends you
I am here in Northern Virginia and got my JK in Dec '06. We had several storms with some wet heavy snow, one about 8 inches. My top sagged a good bit but when I brushed the snow off it went right back into shape. Didn't have any problems. It was very easy to push the snow off in big chunks with a broom.