[Tuor in Gondolin]

If they stay in the clearing it's quite conceivable
the Black Riders would break in and quickly overtake
them (or come the other way going around and then south
after going past the High Hedge) whereas that's impossible
for horses in the Old Forest. And if you look at the maps by
Strachey or Forstad (if the former is still in print) if you
assume the Old Forest is navigable it's pretty much a
covered, straight path to Bree.

Btw, a possible plot hole is the Bucklanders apparently
being totally unaware (unless I forget references in LOTR)
of Tom Bombadil, especially since he must have been not
infrequently in the eastern Shire rapping with Farmer Maggot
since I can't see Maggot's wife letting him traipse off to some
foreign place across the Brandywine.