All of the specifics depend heavily on the individual dog. My dog was actually bred to be able to run with horses, so even though he's small, he keeps up well on rides. He does best when the climbs and descents are smaller and the terrain is flatter.
I still have to pay very close attention to him when I ride with him. He can't go as fast as I can on the descents, even though he can destroy me on the climbs. He's sensitive to the heat (esp when his outer guard coat is in), like your dog, so his summertime trail outings are all hiking-oriented and usually include cooler, higher elevations or spots he can splash in cool streams.
You do need to watch for long term issues, too. Exercise tends to be best when it's moderated, because repetitive stress injuries and overuse injuries are the real deal. I have some of my own and as mentioned above, dogs will get them, too. So even though your dog might
seem fine with the activity level you've chosen, you need to be very sensitive to your dog's condition. Moderate your ride intensity with your dog in mind, not your own conditioning. Monitor how your dog does
after the ride, too, because that gives you a good idea of how the ride was for your dog.
I don't think going to the dog park afterwards is a good idea, either. Your dog is probably plenty happy after your ride and going to the dog park just sustains that arousal level for even longer. Your dog does need some rest after that ride. It takes my dog some time to wind down after a ride. He doesn't crash out immediately. It's not because he isn't tired. It's because the adrenaline and endorphins and everything take some time to flush out. Oftentimes, we get home from a ride and he wants to play more at home. What he needs is to rest, and when he does settle down, he's not going anywhere for awhile.
Here's his full shaggy coat.
As I said before, I have to watch him closely when I'm riding with him. When my wife and I are riding together, we're training him to run between us. He's taking to it pretty quickly, actually. That way the forward rider can be the check on him running too far ahead. And the rider in the back can make sure he doesn't stop for a sniff for too long or make a wrong turn at an intersection, and also monitor his conditioning. We take frequent breaks for him to geat a drink and catch his breath. And for longer rides, we also give him a little snack break because little dogs don't have super deep energy reserves. When I ride with him solo, I have to pay extra attention because it's only me keeping an eye on how he's doing.
The usual loop we do with him is 9.5mi and that definitely works him hard. Other folks use that loop with their dogs sometimes, too, and we've encountered a few. I think a 5mi loop would be ideal to increase frequency for him. 9.5mi is enough for him that I don't want to do that to him too often.