Anto, I have lived in NYC, Boulder Colorado, Casper Wyoming, and Steamboat Springs, so I know about "freezing hard". I've had winters where it froze hard in November and didn't thaw until March!
And whilst I don't mind some cold weather, I used to hate the short winter days. Even when I was in school, we'd go and come home in the dark. Doing that for months takes a real toll!
So no, I don't get "fed up" with sunny weather, because I've earned it!
I chose Australia for that reason. Thirty years ago in my first three months in Sydney, it only ever rained at night! I thought I'd died and gone to heaven!