Bringing the doggy definitely makes choices more limited and puts more strain on you physically and mentally as you go.
Hiking/bushwhacking was so much extra work as he is so small and some of the areas are so steep and rocky. Quite a few times I just had to lift him up a ledge/rock or carry him over some debris.
My small dog is coyote and bear bait. I had to have him ON my hip at all times. I couldn't tie him off to a tree or anything for even a minute as he can get snatched up really quick. When I was stationary, I'd hook him onto my belt. Remington makes a really cool reflective leash with an adjustable length and a caribiner built into the design.
My other dog I go out with is a large treewalking coonhound, but his size and strength carry a different set of advantages and dangers on the trail. If you want full freedom, either don't bring a dog or bring one that is extremely well-trained and built for your particular adventure (mine is not). If you want a really enjoyable time with your best friend at the cost of hauling some "extra weight" around, it is well worth it.