Our fence posts were 6" diameter from TSC. I don't know about t-posts, but I know you want the fence to last and not have to repair it next year. Why put up a fence you keep having to build over again? Another thing- when temperatures are this cold, the ground is really hard and difficult to dig post holes and tamp. We like to wait till warmer spring temperatures and moister soil conditions to do fencing work. My brother-in-law's family was in fencing and they used the cedar on the land to make their posts. I think they cut it and seasoned it before using. I've seen fencing material on Craigslist- sometimes stuff lying unused, sometimes old fencing to be taken away. It can work, but it is a lot of work...
You really need the 6.5' T-posts to have enough to plant in the ground. With a 5' post, you'll only have a foot in the ground. One long T-storm or a couple of really wet days of rain water to loosen the soil, coupled with a goat standing up on the fence, and those T-posts will fall right over. With the 6.5' posts, you can sink 18-24" of post into the ground and still have a little post above fence line that you can put a string of hot wire on top if you find the need down the line. https://www.tractorsupply.com/tsc/p...d-t-post-6-1-2-ft125-lb-per-foot?cm_vc=-10005
For a shelter, I’d do something similar to the pic. That way two goats can cuddle together and will have more room when it rains. You will probably want to have an actual floor though, the first will get gross quickly.
How long are you wanting to keep the goats in the 15x20 pen? Nigerians will be better than Nubians in this type of situation. Nubians get big (our doe has weighed of to 165 pounds). They have a LOT more poop, not trying to be gross but when keeping goats in a small pen you have to think about these things. Their feet will churn it into a mud pit once winter hits. Plus they will be costly to feed. Nubians eat. A lot. They will essentially be in a dry lot, so you will need to provide ALL feed and hay, they will not have adequate forage so that means more $ spent in hay and feed.