Tight corridors is usually the issue with mounts underground. Interestingly enough, the utility power for the horse ranger in the article helps them bypass the normal downsides of squeezing once an encounter, so it certainly seems designed to help with that issue.
Now, if you get to a small enough hole that your mount cannot physically get through it... that's a problem. Or, say, you need to drop down a 30' hole or something. You might be able to work out some sort of rope pulley system, but are probably off investing in some magical options.
A charm or ritual to shrink the horse, for example. Or convincing your mage to cast Slimy Transmutation on your pal, and convincing him that he's better off staying like a frog for a few minutes than trying to fight it off. And hope you don't have a horse explode out of your pocket halfway down the winding stairwell!
Or train your pony to enjoy resting in your wizard's Leomund's Secret Chest (he bought a stable-sized one, right?) Summon it before you go down a hole, have the pony hop inside, and then resummon it down below so he can rejoin you.
In general, I expect you can probably get through 95% of adventures without running into a scenario where your mount will be really unable to proceed. And if you can figure out in advance a few tricks to help you in those situations, you should be able to do just fine.