So let me lay down the background before I get to my main point.

Let's call my villain Rickshaw. He's a barbarian warlord, and he likes dogs. There's different kinds of canines in the setting I'm writing this for; we got the basic dogs like mastiffs and wolves, we got dire wolves, and an intelligent kind of wolf that speaks common. The last is rare because their intelligence gives them an abrasive ego which makes them all hate each other, being lone wolves. Rickshaw isn't the average raging meathead people expect from barbarians. He's quite cunning, and it's his cunning that led him to the idea of using hounds. They breed and mature quickly, are fast and strong, you don't have to equip them to give them killing potential, and enough of them will rip a village to shreds with only a few soldiers accompanying them. It's quite easy to get yourself an army of ravenous beasts, if you're dedicated enough.

So the final dungeon is his keep. I plan for the players to reach it at level 10 or so. He's a master of the hounds, and if he's pushed back to his keep he's going to throw all the stops. Considering mastiffs, wolves, dire wolves, and the homebrew wolf I made all are CR 1/4 to CR 2, I have to wonder. Just how many stinking dogs can he reasonably keep within his keep? How many encounters do I want them to fight through, featuring mostly dogs? How many would he reasonably be able to directly command by barking orders? How many minions is too many to feasibly manage gameplay wise? I know I can just have like 40 wolves in the room with him during the final fight for a properly deadly encounter which he directs in squads of five, but can covering half the room's floor with enemies be more than just a big slog?

Lot's of wolves would be a major slog, and honestly having a ton can make the encounter guaranteed to be deadly since CR rating isn't really accurate when dealing with hordes. More or less it is subjective and based on some factors such as whether they utilize pack tactics, generally act intelligent and focus a single target, etc. It also is dependent on the majority of the dog's hit dice and whether or not you any of your players have big AoE spells prepared or not....cause a fireball could effectively render that portion of the encounter quite easy if initiative rolls are in your players favor.

Horde based combats are basically really difficult to do right in the end though, and it typically is something that needs to be tailored to the group you are playing with. That still said, 40 seems super excessive, especially considering the likelihood that you will successfully surround a target and get some hits off. Now 40+ over the course of the dungeon would probably be fine and help exhaust some resources, but all at once would almost certainly just murder your group. That said if you have your players character sheets you could always do a test run of the first few rounds of the encounter to determine how deadly it actually is, and in this case I would highly recommend it.

Agreeing with the above comment 40 wolves would be excessive. Maybe have somewhere around twenty and some sort of larger/harder to beat dog depending on the level of your players and how many of them there are. If your villain is a hound master he who loves dogs so much he would have had 50-200 of them, he instead found a rare large one such has a ceberus or a beefed up smaller dog that is now much harder to beat. 

There are other ways of skinning a dog than taking a longsword to his hide. 

If it was me, I would have an outer courtyard or similar filled with these dogs and see what the PCs come up with to get past them.

Once they enter the dungeon/building proper they have to start rolling initiative, but until then it's time for a cunning plan. Theirs. Not yours. 
I run two groups, and being surprised by events is always entertaining.

I agree with what everyone said up top, but if you want the idea 'holy crap, that's a lot of dogs' you could adapt a swarm monster (I'd go with rats or quippers), and amp up their size and damage. about 6-8 swarms would be manageable and possibly capture the sheer number of dogs you are discussing.

I just have a hard time being struck with fear at someone named the Quippermaster. I would probably make fun of them and call them the Quippersnapper.

I would probably do something like DuffPhD suggested for the mass amounts of dogs and then give them the pack tactics buff since they are in large packs and then once you enter the main chamber to fight Rickshaw maybe put in a couple of winter wolves (or a wolf/wolves with a heightened CR)  as his most loyal pets and then have a few more wolves and guards. It would get kinda of tedious and dragged out if you sent a massive swarm of low level mobs at a group especially if the dice are not in their favor. Also another thing that you may want to do is think of how many dogs is it actually plausible to raise. You have to account for training, maturity time, group behavior, how many many will the alpha's accept into their packs and how many people does he have training the dogs? (That is if you want to keep a sense of realism.)