Rather simply, the wind is too strong to walk or jump into, and changes directions. The most surefire way to not get blown out of the tree is to open your journal when you hear the wind pick up (j). Wait for the wind to die down, and then just close your journal. You will fall straight down regardless of momentum or height you had before opening your journal. Depending on risk tolerance, you can get upwards of 4 platforms before needing to reopen your journal, and a few less if you pick things up.

Of similar note, picking up objects temporarily cancels out the wind, but as soon as the animation is complete the wind has full affect on you.

If it helps, the blue arrow signals the direction I was traveling in the wind before opening the journal, and the red arrow signals where I will fall once I close the journal (assuming the wind has subsided, if the wind is blowing when you close your journal, you will start to fall straight down but be impacted by the wind on the way). In addition, holding arrow keys as you fall will affect your fall normally.


UPDATE: Per the comments, it appears that opening your map or inventory has the same effect. Use whichever key (j, i, or m) feels the most comfortable :)

If you want a bit more of a challenge, just remember to not get greedy with how many platforms you take at a time. Try and spend the actively blowing periods on a larger platform when you can run into the wind (you will still lose a little ground). I would personal advise using the journal trick, as you will return to these treetops multiple times and the climb back up can certainly feel tedious If you fall multiple times per visit.

Also, if you pick up an object, you will be temporarily unaffected by the wind for the duration of the animation.

If you are about to fall, open your journal. If you think its cheap, jump back to the starting platform and "start over", but at least you don't have to climb back through Honeywood Forrest to get back up here.