You absolutely can. You are free to play any cards in your hand during your turn*. Many times it is the best strategy to play down to 3 cards in your hand so you can draw 2 more. This is especially true if you have colors you don't need, or are playing a standard Mage with a few strong cards in your deck that you need to cycle to quickly.
*Unless blocked from playing cards by specific effects, like "Spirit of Earth", but you can still play cards against an obstacle even if you can't apply the damage (such as against "Gunslinger Adept").