That must have been a beefy 486, as I remember I had trouble getting a Pentium 100 Mhz Toshiba laptop to play mp3's on Linux kernel ver 2.4, and it could only do so from the bash shell without XWindows running. It could manage it on Windows 98, though, but only with the windows media player, if I remember correctly. Winamp 2 was a bit of a CPU hog for some reason, even though I never used visualizations.
I played mp3s on a 486dx2... I think at 40MHz (but could be after 100MHz upgrade). The biggest issue was bitrate, I think it struggled with 128kps but was fine if they were encoded anywhere below. Certainly could not play 160kps. 96kps mp3s were common enough on the internet back then with dialup, although they sounded awful.
Now, if you did anything on the computer other than let WinAmp play without the flame graph, it would stutter. I had the machine under my desk and used VNC to connect to it and change tracks or whatever.