Exactly. I do the same. My dogs have their own machine and their bedding is cold washed purely because it is outside and only connected to the garden tap. I always do a full wash and two vinegar rinses for them though.
Always cold. We actually had the hot water tap removed from the laundry, so you can only use cold in the machine. Occasionally, for a few select items, I will hand-wash them in lukewarm water, but I never use hot.