I will take thick cover for trailing over open fields or woods any day. Wounded deer tend to take the path of least resistance. If a marginal shot should occur, I would suggest taking up the trail immediately. BUT, only go a short distance. Just enough to establish a direction of travel after the initial "bolt for cover".
Please keep in mind this is only a suggestion. A lot of factors can play into the decision of when to follow and when to just back off. Shot placement, how heavy rain is(or gonna be), knowledge of common escape routes, ability to track, coyotes..... You get the idea.