You are correct. Plains are the easiest terrains to explore in terms of time required to do so, and your party's speed is the other factor in how quickly you can explore and travel.
Also note that you need to explore a hex to have any ability to locate features that aren't landmarks. Simply entering a hex will not reveal a feature that isn't massive and/or immediately obvious.
The lesson? Keep your horses alive and in good health!
Reprinted from Kingmaker #1: Stolen Land:
Traveling (Time to cross 1 hex)
Party Speed --- Plains --- All Other Terrains
15 feet --- 11 hours ----- 16 hours
20 feet --- 8 hours ------- 12 hours
30 feet --- 5 hours -------- 8 hours
40 feet --- 4 hours -------- 6 hours
50 feet --- 3 hours -------- 5 hours
Exploring (Time to fully explore 1 hex)
Party Speed --- Plains --- Forest/Hill ---Mountain or Swamp
15 feet -------- 3 days ----- 4 days ----------- 5 days
20 feet -------- 2 days ----- 3 days ----------- 4 days
30 feet -------- 1 day ------ 2 days ----------- 3 days
40 feet -------- 1 day ------ 1 day ------------ 2 days
50 feet -------- 1 day ------ 1 day ------------ 1 day
Generally speaking, I will allow you to enter and explore a hex in one day so long as you can move quickly enough.