We live in newer construction with a hot water heater that is approximately 2 years old. Both last winter and this winter, we have issues with lukewarm water in the showers. The other faucets (kitchen, bathroom, bathtubs) have no issues. If we run the dishwasher overnight within a couple of hours of morning showers, the shower water is sufficiently hot. However, at any other time of day or if we don't run the dishwasher, the shower water is lukewarm at best. The only difference between the showers and the other faucets is that the showers have some sort of temperature regulator required by code.

The hot water tank is indoors and this problem only occurs in the winter months. I could maybe understand if this was occurring at all faucets or with just one shower or if the tank was outside in the garage, but I'm at a loss here. Any ideas? The brand is Bradford White.

The hot water tank doesn't care what temperature it is outside, or inside. It appears to me that you are getting cooler water to the shower that isn't getting to the other faucets, or it may be, but the other faucets don't have temperature limiting devices that keep you from turning the handles further to compensate. If everything is fine after you run the dishwasher, then the problem isn't the tank. Normally, after you run the dishwasher, you will have less hot water. Your problem is that your pipes aren't insulated, and they are ice cold and sucking the heat out as the water is running. If your pipes had been insulated properly, you wouldn't be reading this now.

i honestly can't imagine what the dishwasher has to do with the shower water???
about the showers.. if you have limit stops set on the showers, this will limit the distance you can turn the handle/s. when the cold water coming into the house is relatively warm (summer) you will get a blended hot and cold water that is comfortable. BUT, when the incoming cold water is too cold then the blended temperature will be cooler.
hopefully a simple adjustment of the limit stop will solve this problem.
the danger here is that in the summer when the incoming water is much warmer then the maximum temperature of the blended water could scald you..

Do you live in a house or condo ? Many condo's and apartments use the domestic hot water for heating with a hydro air unit. If so the water may have a cross over thru a bad check valve on the heat loop.