Is it bad to live in a cold climate with raynaud's?

Worse. Raynaud's disease or phenomenon is an exaggerated response to cold in which the peripheral circulation (mainly fingers, toes) is shut down to reduce heat loss. It can also occur in warm environments but is worse with cold exposure.
It doesn't help. It doesn't help, but protection from the cold and appropriate medications and assuring any underlying problem is recognized and treated should help.