Well, first off, the way these are templated is wrong. It'd actually be as such:
Sample Bear One
G
Creature -- Bear
Forestborne 1 - When CARNDAME comes into play, put a +1/+1 counter on ~this~ if you control one or more untapped forests.
1/1
It'd be an ability word rather than a keyword (see other similar examples, such as Threshold and Hellbent). This also solves the templating problems for instants and sorceries.
I think the biggest problem with this mechanic, though, isn't the templating - it is what it is. I mean, Sample Bear One is not exactly an interesting card. Sure, you can play it on turn 2 as a 2/2, but you could also play a Grizzly Bear on turn 2 for the same cost. It fundamentally increases the cost of the card artificially, and the difference between this and actually adding +1 to the cost is marginal a fairly high proportion of the time. While higher costs add more to the differentiation, really this is reminding me a lot of Kicker cards. This doesn't really feel like a good mechanic; it feels awkward and unnatural.
Permafrost Infusion
2U
Enchantment -- Aura
Enchant tapped land
Enchanted land doesn't untap during its controller's untap phase.
This card is unprintable. This is Stone Rain, except in blue.
3wW
Creature --
3/3
w, T: Tap target creature or land.
A strictly worse version of this card appears in the core set. Additionally, White doesn't really get to tap lands. I don't think obsoleting the card in the core set is a particularly good idea.
2R
Creature --
3/3
Whenever ~this~ attacks, tap each land you control.
While cool, I don't really see what this has to do with the mechanic.
Land
T: ~This~ becomes the basic land type of your choice. (This effect doesn't end at end of turn.)
I don't really see what this has to do with your mechanic, and this card is way too narrow to be really useful.
Land
1: ~This~ becomes the basic land type of your choice until end of turn.
This is a cute variant on the land that they printed in Lorwyn, but it feels too similar in functionality (though this is obviously stronger).
Land - Forest
1: Flip ~this~.
Land - Island
1: Flip ~this~.
Land - Mountain
Plainscycling R
These are both strictly better than basic lands and are thus unprintable as such.
Land Creature -- Mountain Elemental
0/0
Mountaindweller 2 - Put a +1/+1 counter on ~this~.
(As this comes into play, if you control another untapped mountain, put a +1/+1 counter on ~this~.)
Why would I ever want to play that card?