During the middle of vanilla, the record for fastest 0-60 on a brand new server was around 7 days /played. So almost 170 hours.
Now most people were leveling alts with a few pieces of twink gear and gold and not from scratch, but then they probably weren't as efficient as the level racers on the new servers. So let's just say 170 hours on average.
If you played your alt 40 hours a week like a full time job, it would take you over a month to reach cap. If you played 20 hours a week just on your alt, it would take you 2 months. Not as long as some other MMOs, but much much longer than leveling today.
I'd reckon those that had more than 2 level 60's in vanilla were putting in some crazy hours in the game. I personally only ever had 1 max level in vanilla.