Boetticker was attache.

Yes, in this picture it is largely style/tradition although in the 1930s there were still some actual horse cavalry units still in operation. So there would be some utility for some officers.

I do not believe General Short was in the cavalry so this I would imagine is a fashion/tradition holdover unless they were using horses that day to observe the war games over uneven terrain. AFAIK once actual horse cavalry were no longer a thing in the army you don't really see the jodhpur anymore, especially as that generation (think Patton) moves on.

Edit: it's August j22, 1939 (says right in the post, idk how I missed that). So prewar by American standards and most European standards although Germany invades Poland in just 10 days kicking off ww2 in Europe.