Horton Creek Trail on a Friday should be fine. As with anytime you are hiking with dogs off leash, have a leash ready if you run into somebody else, but I wouldn't expect much traffic on a weekday. It will be relatively hot there, but the creek will allow the dogs to cool off.
As others have said however, going up on top of the rim might be a better option given the warm weather right now. An old favorite is the Cabin Loop (the best leg is the Houston Brothers Trail). It'll take you an extra hour of driving past Payson, but its a great area, and should be a more temperate hike right now. I'd be surprised if you saw a single other person on a Friday, and the dogs would love it.http://hikearizona.com/decoder.php?ZTN=62http://hikearizona.com/decoder.php?ZTN=797