I used a 36" screen door on our high-tunnel and mounted it on the outside. I made a sliding door on the inside from a closet door track on a 2x6 frame and sealed it with garage door seal. I didn't worry too much about the screen door. But in your case using a storm door you could just put simple door weatherstrip around it from Home Depot / Lowe's. I'd consider an interior door though if you in northern areas. Another option would be to hang plastic over the door over lapping the edges like a curtain.

I have been thinking about adding two small walls and a short roof around the entrance as a wind break though.

Thank you for the ideas. I will probably use weather striping since I already have it.

I recently made an improvement by adding three 4x10 twin wall corrugated polycarbonate panels covering the top and the upper portions of the two sides - the old plastic sheets were partially torn. I can feel that the entire structure is more strong and stable.