Say I have a Blinkmoth Nexus and Steel Overseer out. I tap the Steel Overseer for his ability to put +1/+1 counters while my Blinkmoth is a creature, and it gains a counter. After my Blinkmoth goes back into a land, does it keep the counter, or does it lose it?
Lands (any permanent, really) can have +1/+1 counters just fine. In fact, Llanowar Reborn enters the battlefield with one! The counter(s) will not go away just because your blinkmoth stops being a creature.
Of course, the +1/+1 counter doesn't do anything until the land becomes a creature again, but the +1/+1 counter will still be there.
Yes, the permanent keeps the counters. Nothing causes them to be removed.
There are only three instances when counters are removed from objects by the rules:
- Dealing damage to a Planeswalker removes loyalty counters.
- SBAs cancel out +1/+1 and -1/-1 counter pairs by removing them.
- SBAs remove extra counters when a permanent has a limit to how many of a given kind of counters it can have.
That's it. Counters are never removed from objects except in those circumstances or by abilities that instruct you to move or remove them.
There's definitely no restriction about which type of counters can be on which type of objects.
- You can have +1/+1 counters on non-creatures.
- You can have charge counters on non-artifacts.
- You can have flood counters on non-lands.
- You can even have counters on non-permanents!
When an object changes zone, it ceases to exist, and so do any counters on that object. They are physically removed from the physically object (because they ceased to exist in the game), but they are not removed from the object as far as the game is concerned. Abilities that would trigger on counter removal don't trigger, for example.
121.2. Counters on an object are not retained if that object moves from one zone to another. The counters are not “removed”; they simply cease to exist. See rule 400.7.
This includes three keyword abilities that remove counters:
- Fading (fade counter)
- Suspend (time counter)
- Vanishing (time counter)