Most important reason to pee before you go to bed: you'll be uncomfortable lying there all night feeling like you have to pee.
Second most important reason: if you try to delay it, you'll just have to get up later, in the middle of the night. This means getting out of the bag and getting cold.
The REI blog sounds scientifically illiterate to me and does not appear to be backed up by a citation of any scientific source or any experimental evidence or valid theoretical argument.
When your bladder is full, your body is expending energy keeping that liquid warm. If you empty it out, your body needs to expend a little less energy to stay warm.
This sounds like the blogger didn't understand thermodynamics very well. The rate at which heat flows out of an object by conduction into its colder surroundings is proportional to its surface area and to the temperature difference. When you surround your body with a sleeping bag, the rate of heat flow by conduction is also inversely proportional to the thickness of the bag. Having a bladder full of pee at body temperature doesn't affect any of these three variables, so heat will flow at the same rate when your bladder is full. However, when your bladder is full, it will add slightly to the amount of heat energy that your body starts with, so heat loss at the same rate will produce a slower drop in temperature. In reality I would expect this to be a small effect.
We could also worry about heat transfer by convection or radiation, but I don't think it changes the conclusion.
Your body does not, of course, spend the whole night coming into thermal equilibrium with its surroundings. It probably maintains its core temperature at close to nominal body temperature, but body parts like skin and fingers will get colder. Your body is probably in a steady state of heat flow for most of the night, with its metabolic heating staying in equilibrium with heat loss. I don't think this alters the conclusions, because the rate of heat loss is still governed by factors that are pretty much the same as in the description above for something just passively cooling.