Bit of an update: I disabled the Skyrim Flora Overhaul to see if that was causing it (the mod author says that 1.5GB of VRAM is required, I only have 1GB), and the gameplay was a lot smoother. After playing for a good 30 minutes, I was having no stutter while running around Whiterun on horseback, which never happens.
However, I alt+tabbed the game to check what time it was, and when I went back to it, it froze a mere 10 seconds later.
I'm using SBW to make the game run in a borderless window, maybe that has something to do with it, somehow? Although, I've used it before without a problem, it was just recently that it started freezing like this, just after adding all the STEP mods, ENB, and RLO.