All the usage examples for impromptu I could find in a couple of dictionaries involve actions (impromptu speech, wedding, etc.) Is this a general rule, or can I talk about an "impromptu field hospital"?
The nuance about 'impromptu' is that it usually refers to something not so serious, and so it is very slightly incongruous with the more weighty 'field hospital'. But it is not glaring and so it could work. It is not discounted because it most often goes with actions or events (because one could assume that one is taking 'field hospital figuratively for its temporary construction). But the slight incongruity of register really is hardly noticeable. If you continued in a lighter vein about the rivers of blood and maggotty battlefield injuries, ha ha ha, it would work perfectly fine.