The Finnish variant is a Stiga Jet:
https://www.youtube.com/watch?v=IdiPmYSTwlU
(The video starts pretty slowly, and doesn't provide much info about how that was built, but it looks fun. There are also plenty of more scaled-up projects, basically looking like combining a ski-doo with a V-1 rocket).
(I actually used a kicksled in the winters to go to school, until I got a moped.)