It depends on what type of bladder it is most likely. I have a CamelBak Thermobak and the documentation that came with it stated that the bladder could be partially filled and frozen.

However, I think the problem might be with repeated freeze and thaw cycles as might occur in a bladder stored outside in a New England Winter. If water should get into the non-flexible parts and then freeze I would worry that the resulting expansion could ruin the gear.

I'd just leave the bladder empty and store a container of water that might better hold up to repeated freeze and thaw cycles with your BOB. You could fill the bladder from the water container later, provided it wasn't frozen.