Fun game for the 1 button! Here is some feedback to help you in the future:
Pros:
-The art is really well done! The background especially gives a feeling of depth to the game despite it being 2D.
-The game is challenging but actually a lot of fun. The way you implemented the high score mechanic was great, would be cool to add a leaderboard in the future but I liked that it saved my score so I could keep trying.
Improves:
-Adding some sound would great. Even just a jump sound would immediately make the game more immersive, but also some country-western music in the background would be nice.
-The arc followed by the cowboy just felt a little off. I would refine that a bit. Almost felt like he came down to quickly and didn't have enough float.
-For the use control I felt that it was a little weird to have the space bar "release" be when the jump event occurred.
Great game for the jam!