When I first started playing Sylestia, I played on mobile.

For the arrow buttons, you have to tap them on your screen.
If the button is greyed out and not blue, that means that direction isn't currently available because either an obstacle, such as a bush, is blocking it, or because you encountered any enemy or something you have to interact with, and need to choose one of the available(Non-Greyed out) options below the explore screen(Interact, Battle, or Ignore, exit zone is just to exit the zone.)

When you first enter the explore zone for Spring Fest, you can only go down the first time you make a move since up, and both sides are blocked off.
So, basically, to explore on mobile, you'd tap the arrow buttons that are blue, if they're greyed out, that means that direction isn't one currently available to go. You'd just have to hit an arrow that's blue to continue moving.

I apologize if the explanation isn't the best. ^^;

Nope that was very helpful thanks!

You're welcome!

Oh, a little add on, occasionally if my internet is running slow(It still happens now on my Chromebook), or something like that, when I'd press an arrow, it would sometimes not load properly, and I'd have to reload the page. So that could possibly occur as well, and cause you to be unable to move.
A page refresh should solve the problem in that case though. ^^