A pug was an extreme example to make it obvious for folks like you.
The only thing made obvious for me is that you can't grasp a concept, and that might explain why you can't seem to get dogs that can run in -35 temps the way you want them to. Exactly where is the science that tells us that even though most all dog breeds share the same amount of scent receptors, not all of those receptors are developed equally? I didn't think so. You don't have the science on it and I doubt you can Google it up if you spend all day trying. This baloney about good nose/bad nose is what you've told yourself is the case, and it is you who cannot see the obvious.
The REALITY is, a Golden Retriever, a Rottweiler, a German Shepherd, a Doberman, and many, many other breeds - even mixed breeds, can smell just as well as your beagle. 220 million scent receptors is 220 million scent receptors, period. A Newfie can locate a drowning victim simply by the very diluted bit of scent that makes it to the water's surface. They use them because they are large enough to haul a body out if need be. We use beagles because they are small and fast. If nose is quite equal among so many different breeds, there is virtually NO DIFFERENCE among dogs of the same breed. The nose-to-mouth connection is
largely determined by brains. It is what tells a dog when it's feasible to claim a line.
Consider the back-tracker. Dogs are at a check. Dog A takes the check out back-tracking -- tonguing like a mo-fo. The other 4 dogs ignore him and continue searching. Is this because they don't have as good a nose as dog A?
Consider the truely, what is loosely called the "cold-nosed" dog. He's out there popping off on scent laid down the night before, and the other dogs are not. Do you think the other dogs cannot smell what he's smelling? Sure they can. They simply have the brains to recognize it as an old track, and therefore don't claim it as a viable one.
Consider the average walkie-talkie brace dog. I rescued one of these one time and had him in the back yard with my other dogs for a while. I would let the dogs down into the yard each evening to exercise. This brace dog never shut up from the time he was put on the ground until I put him back above ground. He barked on squirrel tracks, he barked on my footprints, he barked on all the other dogs' tracks, and at one point...when he'd run out of a track, he turned around and tongued his own track back the side-length of my fence. There's a reason why brace dogs are carried to the line and put down on it. If they didn't keep them off the ground until the moment of truth, nobody would know when the chase really began. Did they breed better "more developed" noses into those dogs? No, they bred the brains out.
So I have to go back to your scenario where your outcrossed female had some 5-minute spurts of "running" and the other 4 did not. I would challenge you that your 4 other dogs smelled exactly what she was smelling. She considered it a viable run and said so. The other 4 didn't agree.
There isn't a nickel's worth of difference in the noses of all beagles. It's all about how they "choose" to use it, and that is brains. You see that dynamic in humans, too.