I deal with Rocky Mountain winters and recommend:
Clean your chrome wheels often with CAR WASH SOAP, not some acidic wheel cleaner.
Keep a coat of sealant / wax on them.
The longest lasting, most durable sealant I have ever used is Finish Kare 1000p High Temp Wax. Before you say something about the name, let me explain. Finish Kare is a company started by Fred Meguiar, who chose to compete with his family's business, "Meguiar's." 1000p is a full synthetic sealant originally designed as a mold release agent. Industry references "mold release waxes," not synthetic sealants so it was named a wax. (Virtually all car waxes are really synthetic sealants. Non-car people look for wax, not sealant. )
It has exceptional durability in both hot and cold conditions.
I clean my custom wheels with a hand held steam cleaner. It's easy and works really well. You can pick one up at a department store for around $30. These are the units you see advertised on TV for household cleaning.
Coat your wheels with 1000p and clean them as often as you can - in a friend's garage if you have to - and reapply 1000p twice a month.
I have also heard of applying plastic coat to wheels for winter. It's durable and the rubbery thick coating protects against nicks and scratches. It is easy to peel off, too.