DIY hot / bath tub in shed?

This is probably a dumb one, but here goes.

I've got a tiny house with one bathroom, and it only has a shower. I love taking hot baths, used to do it 2-3 times a week, more often when I'm sick, and I miss that. I have a pretty big shed in my back yard, think one of those pre-fab things... it's got some tools and stuff but it's mostly empty space. It's pretty close to a hosebib and an exterior electrical outlet on the side of my house, so I've got cold water and extension cord access.

Is it even reasonable to consider ways to set up a tub in the shed? Maybe freestanding? maybe something I build from fiberglass? I'm pretty confident I can drain the water out into my backyard with no issues (big yard, neighbors won't see / care), but is there anything obviously impossible or really stupid about this idea? Is it possible to use an electric water heater or should I figure out something with propane / butane? Anyone tried anything like this before?