No. Your body temperature doesn’t drop because of peeing in and of itself.
Peeing makes you lose a bit of body mass which – all else being equal – can mean that you’ll get colder slightly faster afterwards, if your body doesn’t produce more heat than it loses.
Obviously peeing usually means that you’ll have to remove a few layers of clothing and stop moving for a minute or so. Both factors can lead to your body temperature dropping (further). But I’m not sure “holding it in” helps with this a lot since you’ll just have to pee longer (albeit less often).
In any case, the dangerous aspect which leads to hypothermia and death is that you are constantly losing heat faster than you can produce it. If you are dressed warm enough exposing your bum for a minute won’t be a problem. Your body temperature might drop ever so slightly and then go up again once you are wearing all your clothes. “Holding it in” could actually be dangerous since shivering can easily make you lose control and pee yourself. In which case you’ll be cold and wet …