Rechargable Nickel Metal Hydroxide batteries are available in AA size and would solve your battery issue.
HL 1/16 scale tanks uses a standard 7.2v 1700ma NiCad rechargable RC hobby battery for the tank and only use AA for the transmitter.

I dont know of any of the sub $100 tanks that are weather proofed in any way. Any snow that melts and gets inside is probably going to cause problems.

I am currently undergoing testing of one of the newer HL 1/16 scale Tigers and will keep this board updated of its status.