This came up in my game last week and wanted some clarification.

from the rules guide - "A figure must spend one additional movement point to enter a space containing difficult terrain"

Does this imply that every blue space they go through costs an additional point, or only the first blue space they enter cost the additional point and then the figure can more freely through the blue at no additional cost?

The rules,I feel, implies every blue space costs 2 points. But my players disagree that it's on the first space you enter.

Anyone have a final word on this?

Final word? no, but educated guess based on other things. The FAQ come to mind:

Q: When a large figure moves, does it exit all spaces it occupied and then enter all of its new spaces, even if some of those spaces overlap? A: Yes.

So since you're always exiting a space and entering another space, what the space you're exiting will have little difference. Also it's just logical. The terrain is not any less difficult because you're already in it. If you're walking across a field of somewhat loose large rocks, is only your first step cautious or are you cautious across the entire area?

Bottom line is that each blue square costs 1 extra.

Karrde has nailed this one perfectly

Each time you leave a space you are entering a new space, triggering rules relevant to that space.

A Hindering terrain space doesn't care that you were already in a hindering terrain space.

Thanks for the quick response, I appreciate the info.