Most bridge teachers (and books) teach players to draw trumps at the first possible opportunity. The reason is that you don't want your opponents to take tricks with low trumps. (If they have the A, or Kx or Qxx "offside" your ace, their high trumps will take tricks.)
One exception is a cross-ruff. Then you want to take your top card winners in side suits, before cross-ruffing, so that your opponents can't discard those suits and later ruff your high cards with their remaining trumps.
Another example that was given in a bridge write-up was when you want to ruff low cards in one hand with trumps in the other hand (after it runs out of the suit). If you do this, you leave opposing trumps outstanding. On the other hand, is it true that the act of your ruffing (thus playing trumps from one hand), "qualifies" as a trump play so that you don't leave yourself unprotected? Or put another way, does it often make sense to ruff before drawing trumps?