ours stay out all year. and the guinea pigs.
some in a hutch & I have to carry them out to the run (so they get to stay in when its cold & wet!)
and the others in a huge run with an open-door hutch inside - they choose when to go out and in.
I cover the hutch roof with a piece of old carpet or blanket, and a waterproof eg tarpulin, these get pulled over the front during autumn and winter.
please dont keep a lone bunny. Most people will say that guinea pigs are unsuitable companions, although we've never had any trouble at all with any of ours (at the most, 12 guinea pigs and 7 rabbits, split by sex.... and one buck just with gps as his dad & brother sexually abused him!)
ideally, I'd recommend giving bunny the option of choosing when to go in and out... though the human interaction can be less.
rabbits are not really very keen on being picked up and cuddled, being prey animals.
but will come to you if "trained" (spoilt!) by food