You did a nice job fixing up that stream. I really hate the damage that too much water can do. That being the case I would still take too much water rather than not enough.
Couple of questions:
1) Why go haul wood right after a heavy rain??? I hate making ruts in my farm lanes or fields. So I wait a few days let things settle a little then go at it. Now if there was a more immediate reason I have cut ruts too. Feeding cattle or getting the crop in but just to haul wood in that I would not burn for months. That would wait for better conditions.
2) You have a 4 wd truck but the tires are not very aggressive. Are they snow treads??? We run a lot rougher lug on the pickup tires around here.
Just wondering how/why things are done in other areas.