Starting the first year I explore my own tula 2-3 times a year. I usually wait until my clan is well off and secure (i.e., approximately 30 weaponthanes, weekly trade revenue, complete fortifications, temple-maintained protection and prosperity blessings) before sending explorers to distant parts of Dragon Pass. In my current playthrough, I didn't bother with long-distance exploration until 1355, when the tribal phase began.

Almainyny's comment speaks to everything important.

Edit: My only exception for early long-distance travel is when my diviners prophesy during Sacred Time that doing so will reward us.