Both of your sentences are correct.
East is not capitalized in either of these sentences because it means a direction.
Would I write...
While driving east, the forest became denser.
or
As I drove east, the forest became denser.
Also, do I capitalize East?
3 answers
I will go with Ms. Sue's answer. It could still be either way around.
.The trees did not do any thing as she moved. The better sentence would be the one using "as"