Here's a report from a thrify DIY'er:

Nothing is EVER easy. I was just going to take the wheels off, give
them a nice coat of rustoleum, and repack the bearings...trouble is the
lug nuts haven't been turned in probably five years or maybe more
(three of those are my fault). In my defense the trailer never went
more than 5 mph for about 300'. Anyhow, on my last frozen nut the stud
broke loose and was turning freely. I tried (foolishly) to weld the
stud using a car battery (google'd "welding with a car battery") but
later found out it was hopless. After taking the whole wheel and hub
off it was time to get nasty.

Next up, grind the stud off from the back with a cutoff wheel. No
dice. I was just about to give up and take it to the shop when I
remembered a Google thread that suggested cutting the lug nut off while
trying to save the stud. Saving the stud looked pretty hopeless and
they should be easy to find so I decided to cut straight down on the
stud and bang the bolt off. It worked like a charm. Thank you Harbor
Freight $7 grinder!