Is it possible to seal an interior barn door to provide an acceptable level of insulation between a conditioned and an unconditioned space?
I'm sure it's possible but it sounds like a real mission. sliding doors tend to seal much worse than swing doors but if you're prepared to make a heroic effort and embrace tighter tolerances instead of looser something could probably be done.

For a swing door, 20" is a standard door width but you'd need to cut the height down and repair the cut end, https://www.youtube.com/watch?v=iSLiWCgCATE

I clamp a straight-edge to the door because I'm not very good at cutting straight lines.