what do you want to use it for? What's going in there? Just the washing machine ? If that's the case and nobody's going to be going in and out a lot to check clothes in a dryer or use the loo, then is it worth the expense of connecting it to the house?
We've just got rid of the garage door at my elderly parents and replaced it with a door and 2 windows and partitioned off the front of the garage where the door into the kitchen is. We stuck a bit of insulation in the new stud partition and under the OSB we've put down on the floor, but there's no heating in there and no hot water or sink , so it really is just a room for the washer and dryer and a bit of storage .The sun shines in there all day now ( if it's out) so it's much warmer than when it was the garage and better for my mum/ carers/ us.