wv,
It's just a guess, but I think it would take some pretty cold weather to seriously endanger your bow.......probably much colder than you would want to be standing in shooting an arrow.[:-]
Todays bows are pretty tough pieces of equipment.
I shot 3D on Sunday and the temperature never hit double digits. That's cold, and I didn't even think about it having any ill effects on my bow, and it didn't. It shot great.
There are guys who hunt Musk Ox in temps like 8 million degrees below zero and their bows still perform just fine.......you should be ok to shoot as much as you like in any weather you'd feel comfy shooting in.
I would bet you'll die of exposure before your bow will.