If the battery is Lead Acid ( SLA ) keep it fully charged at all times and it's ok to leave it in the cold..

If it's Nicad/Nimh partially discharge it and bring it indoors, after winter is over, put it on the charger and wait for the green light, put it on the bike, wheel off the ground and run the motor for a while ( it may run for a little bit and quit, or run well, depends on the rate of self discharge and quality of the cells .. but dont expect much ) .. then put the battery back on the charger. Repeat 3 times and should be all good !

If it's Lithium, depends on what you have.. pls advise .. if it's a " Ping " battery, disconnect the BMS, if it's a pre-built in a fancy box instructions vary .. but it's usually recommended to leave the pack partially charged for long term storage.

cold is ok, moisture is not... depends on your location, i know some people who store their packs in a sealed bag in freezers but if you canot control moisture it's best imo to keep it inside for the winter.