After some experimenting, I've found:
If you take a frozen green spring event (not a normal spring that's been frozen), unfreeze it, and then blow up TNT next to it, it works weird, pushing you in either direction sideways. If the spring is placed on a destructable scenery tile, and the tile is removed, the spring can even propell you straight down. If you get pushed down, you tend to be forced to run to either the right or the left on landing. The direction and speed will be consistent if you run into the spring more times, but will randomly change again if you use TNT near it another time. The spring never seems to return to its normal state, no matter how many times its hit with TNT. It works in both single player and multiplayer, both for host and clients, from what I can tell, with the exception of springs hit with TNT before the player joins, in which case the spring will still be frozen.

I'd appreciate it if anyone would verify these results, correct any mistakes I've made, explain any other patterns they find, or explain why this might be happening.