Can I add four 20Amp circuits in a subpanel with a 10-3 feeder?
You have the ideal situation for adding a subpanel. Woo-hoo!

As @Philip points out, you can use any size subpanel you like. Get one that's bigger than the minimum, so you have plenty of room to work inside.

You can choose either a "main lug" panel, which does not include its own main breaker, or a "main breaker" panel. In the latter case, the breaker can be any size, as the feeder is already protected by the 30A breaker in the main panel. 

If the panel is mounted outdoors, it must be an outdoor rated panel.

In my jurisdiction, a pair of grounding rods are required if the garage is detached from the house. If it's very close, you can probably share the same grounding rods as the house uses.

Be sure to keep the ground bus and neutral bus separate in the subpanel . They should only be bonded in the main panel.

Consider adding a 30A 240V recep right off your new subpanel where you can plug in heavy equipment on short notice.