General strategy:

You'll want to mulligan hard for an early game curve. Mad Scientist essentially provides 4 mana worth of value and helps control the board early, so this is a card you'd want in nearly every match-up. Following up Mad Scientist with Illuminator can provide a lot of body and forces your opponent to trigger a trap that will likely put them behind even further. Steamwheedle Sniper is not a great turn 2 play generally; it's best used on turn 4 so you can get immediate value out of its effect. There are other decent 4 drops in this deck if Steamwheedle isn't safe to play though. By turn 5 if you don't need to hero power with Steamwheedle, Loatheb and Sludge Belcher are incredibly good at protecting your board, letting you swing into the late game.

Cards that I didn't add but might be good:

I wrote these in approximately descending order, from most likely good to least likely good.

Big Game Hunter - More hard removal which lets you keep up with other control decks, but also plays on curve against aggro decks. Probably replaces Illuminator.

Explosive Sheep - It's terrifying with Feign Death, basically an Auchenai+Circle combo but for Hunter. I suspect this might become a big Control Hunter combo. Or maybe not. We'll see!

The Black Knight - Tech card that works incredibly against taunts. Sylvanas is just way better due to Feign Death though, but this is still a solid 6 drop that could take the place of a Savannah Highmane.

Loot Hoarder - Now that Flare got nerfed hard, this might end up being a better way to cycle the card in the deck a little bit.

Animal Companion - This might seem like a weird thing to exclude, but consider what you get from this card and it's not so weird. Leokk isn't good because your board will be sparse, and Huffer doesn't help much in establishing board control. Misha would be the best card for control, but getting it is a crapshoot. Animal Companion would work better in a beast synergy control deck.

Madder Bomber - Possibly useful 5 drop. The synergy with Gahz'rilla and Acolyte of Pain is obvious, but even without those cards it could work pretty well on its own.

Tundra Rhino - I didn't include this because I think it's unreliable and a weak play even though it obviously has synergy with Gahz'rilla. I'd rather have minions in the deck that can reliably keep the board clear. If this card survives a turn, it's likely you were winning anyway, and other 5 drops would have been just as strong of a play. But when you're losing, this card has no chance of swinging the game in your favor.

Flare - Before the nerf this was a pretty easy and obvious auto-include not only for the card cycle and effect, but also for the Pyro synergy. Now I'm pretty sure it's mostly a bad card. Oh well. I replaced it with an Arcane Shot for Pyro synergy and Gahz'rilla buff, and a Deadly Shot for taking down big minions.

Cards not needed:

Cairne Bloodhoof - Savannah Highmane is better (tackles through Sludge Belchers) and does essentially the same thing.

Call Pet - Shitty unreliable card. Idiots are going to swear by this card and post screenshots to Reddit when they get lucky and get a nice minion off it. But it's really really bad. You can quote me on that.

Tracking - Not enough room in the deck. Also not totally needed.

Alexstrasza - This is included in Freeze Mage and control Warrior to make the opponent go from 30 to 15 in one turn. But you're a Hunter, dammit, you'll likely hero power a few times throughout the game and get the opponent to about ~20, which would be enough to finish off with a Gahz'rilla that's been buffed twice.

Elven Archer - I think this card is weak and there are better cards but it does serve a dual purpose as a buff and early game clear, so who knows. This card depends on the meta--if one health minions become popular then this card will fit.

Modifications and other ways to play Control Hunter

I addressed a lot of critiques of this deck and instead of modifying this deck too much preemptively, I decided to make a completely new deck. The two biggest differences are that it is a slower deck and it does not rely on secrets:

I hope this inspires you to build your own Control Hunter deck and make adjustments as you see fit! :)