To understand how to counter any threat, you must first determine what the threat is capable of, what it is used for, and what techniques your enemy will use to achieve thier goals. What you should not assume is that that these tanks will be engineered to specs that make no logical sense, or that they will just charge into any situation like mindless drones. To effectively counter any enemy, you must first assume there is atleast a basic level of intelligence behind your enemy's actions.
First, let's look at how a smart enemy would engineer these tanks.
A lot of answers so far speculate about the mobility of these tanks, but I will try to go more into actual numbers to solve for if you CAN make a reasonably mobile medieval tank. I will go with 2 draft horses because a 3-4 horse tank will not be able to maneuver around the sharp turns you find in many medieval roads, and a 1 horse tank is far less efficient, and would have a very hard time moving the weight of the tank even on paved roads.
To enclose 2 horses, and leave them enough room to walk, you will need a box about 300x200x400cm for the body of your tank. Which is roughly 3,500kg of steel. You will also need a turret which will need to be about 150x150x150cm to seat a single gunman and a driver. This is another 850kg. A Gatling gun with ammo is about another 100-150kg. Your wheels and wooden frame is looking like 600-1000kg depending on how many wheels you go for. Your 2 riders are another 125kg
Add this all up and you are looking at a tank that weighs roughly 5175-5625kg.
The maximum sustainable wagon load on a paved road for a pair of draft horses using historical wagon design and road paving techniques is about 10-11 tons; so, we can speculate that these tanks can travel on paved roads just fine, but medieval warfare often means traveling over unpaved terrain.
When you take a 2 draft horse team off road, thier wagon pull capacity drops down to about 4-7 tons on mostly flat dry dirt or grass and 1.5-4 tons on poorer terrains such was muddy, uneven, or sandy terrain; so, the only places these tanks will really be able to travel will be on roads and generally flat, dry, solid terrain.
How to make these tanks more practical
That said, your 10mm armor speculation is way overkill for most of what you need. Most medieval weapons (bows, crossbows, etc.) could be blocked by 2-3mm of steel. Even the muskets of the time could not pernitrate more than about 4-5mm of steel... that said, you may occasionally need to face swivel guns which could require closer to 20mm of steel to block. Larger medieval cannons than this are no threat to a tank because they could not be aimed well enough to be used on anything other than large stationary buildings or naval ships.
With this in mind, consider that nearly all tanks throughout history have not had uniform armor thickness; so, neither should these. Instead of a consistent 10mm hull, you should rate each face to deal with the most likely threat you'd face from any given angle. To this end, I would suggest rating the front of your tank against cannons with 20mm armor (or perhaps 10mm of steel backed by 50mm of wood for the same weight more like a mini ironclad warship.), the flanks against heavy muskets with 5mm armor, and the top and back just enough to deflect muskets hitting you askew and to stop a melee attacker from breaking in with 3mm armor.
So, instead of ~4350kg of steel, the tank could defend itself pretty well against all probable attacks with only ~1475 kg of armor.
Also, adding more or wider wheels will not help because it is the co-efficient of friction you need to overcome here, not a lack of traction. In fact, in most cases, adding more wheels will actually slow you down because horse drawn wagons do not work on the same principles as a self propelled vehicle; so, 4 wheels will likely be best since they will reduce friction and weight compared to a more tank like wheel setup. This related answer goes a bit more into detail on this. Fewer wheels means you can go with the lighter frame estimate of 600kg instead of the heavier 1000kg I mentioned before
This reduces the total weight of your tank to ~2300kg making it able to travel even in "poor" terrain. If you go for this more realistic armor distribution, then the tanks could join your army in a much wider range of battlefields. This would put the weight of your tank at less than a typical, fully loaded, medieval supply wagon meaning anywhere a typical army can go, so can your tanks.
How Would Medieval Tanks be Used
A lone tank is an easy target, but a if supported by infantry and field engineers, they would be almost unstoppable. The initial use of tanks would probably see tactics emerge that are somewhere between using elephants and war wagons. Warwagons were very tank like, but they did not protect the horses because they needed the whole internal space for solders, this made them static defenses on the battle field. These tanks however only need 1 gun man so you can put the horses inside the wagon allowing it to move around while fighting; so, they could advance during a battle to break up enemy lines like a war elephant. Ideally, they would move in advance of your infantry (no need to charge at full speed risking unseen traps, etc.) while shooting up the enemy's front lines. Chances are this would make any medieval army break on its own, but if the enemy are very disciplined and try to encircle your tanks looking for some weakness to exploit, your infantry can then move in and easily dispatch those enemies since thier battle line would be broken.
As for when the army is on the move, you would keep your tanks in the middle of any troop columns. This way obstructions, traps, and ambushes can be identified and removed before your tanks even reach them.
How Would Medieval Tanks be Countered
Medieval armies were not good at countering war wagons to begin with. To up-the-anti to machinegun wielding, mobile battlements... it it unlikely that any medieval army would stand much of a chance at all. You could flood terrain or try to make traps to kill the horses, but even when fully stopped, a few magic machineguns could still control the battlefield just as much as war wagons did... only better. Also, killing the horses is only a temporary set-back. Horses can be replaced much more easily than the tank itself. You can try to fire bomb them, but again, those machine guns, plus the support infantry would make getting into range for this VERY difficult. You could try to shoot them in the backside with muskets, but this also means getting past the support infantry.
The only real counter would be to build bigger, stronger, aim-able cannons able to overcome any wagon's front-side armor. In our history, Pivot guns (larger cannons that can be turned to aim) did not come into play until the late 1700s, and did not become common until the 1800s...but in our history, we did not have a huge need for them. The threat of tanks may very much accelerate the development of such a weapon system. So to answer your question, no weapon or tactic actually used in the medieval period would prove an effective counter to tanks... but special anti-tank cannons could likely be developed to meet the need.