When I connect an LED to an Arduino digital pin, I usually put a 220-ohm resistor in series. However, since the TinyZero is 3.3v instead of 5v, is that still necessary?

It depends on the voltage drop of your LED. Most likely, you will still need a small resistor.

However, if the voltage drop is very near 3.3v, which is quite possible with a white LED, then you will not need the resistor.

Almost every LED has about a 0.7V voltage drop across it. You should always use a current limiting resistor in series with any LED. There are specific resistances for each color LED as the current required for each is different. Typically a resistor from about 300 ohms to 1k ohm will do the trick.

Hope this helps.