Hmm, readying spells while riding? Well, after re-reading the section on readying spells, I would say that you can, but that the constant motion of riding would make it slightly harder, so that readying new spells would take about 1 hour, 15 minutes. You should be able to just about squeeze in that hour and 15 minutes during the ride to the edge of the forest, so that you can have new spells readied for whatever the forest brings.
(just so you know, I based this decision on the info on pg. 164 of AU. Since lack of notes and such can add time to the readying, I think that continous motion would have a similar effect.)