Keep moving if you can't build shelter and fire. Have a space blanket and poncho liner/fleece blanket to wrap up in if you can. Something wind proof and insulating. Your body heat will eventually start to dry everything. I have used a poncho and poncho liner wrapped around my shoulders, sitting on my rucksack, with a small heat source in a hole between my legs (heat tab/sterno/small fire). You have to keep your head out of the poncho (fumes form heat tabs will kill you), and leave a small hole near the ground for air, but it will dry you out and warm you up quickly. It requires little effort or materials.
If you can, get the fire going first, then work on the shelter. Shed the clothes and dry them. I like carrying a super absorbent camp towel, a large one, and rolling my clothing up in it and squeezing as much as I can.
If you know that you are going to get wet in advance, remove your clothing and place everything in a plastic bag to put back on after the stream crossing.
I have had to do winter water crossings many times in the Army. it is never pleasant, but it is survivable.