Spotlight On: Earth Pony Magic

Yes, they have it. I have thought so since 'Hearth's Warming Eve' when a plant sprouted from dirt in Smart Cookie!Applejack's hoof. Now, since that was a play I always took that example with a grain of salt. But then we get Celestia telling us that Earth Ponies have magic in the season 4 finale, and even more crazy, in 'Castle Sweet Castle' Applejack gets plants to grow indoors just by laying down some fertilizer -- on stone floors! So obviously it is magic. Even so, there are a few types of Earth Pony magic.

Strength

So they can work the land, they are physically the strongest of the three main tribes. But in the season 4 finale, once their power is siphoned they can barely move because they're not used to not having magic. An image of being strong is probably also a factor, since in 'Dragonshy' Big Mac struggled to lift Applejack's saddlebags in his mouth, but AJ herself did not. On top of that, there is Pinkie Pie (lifting rocks) and Maud Pie (throwing rocks) to consider.

Endurance

Earth Ponies are not only farmers, but miners and textile workers. Most of those jobs seem to have long hours, and the Earth Ponies must be able to handle it regardless of not having a Unicorn's more overt type of magic. Applejack in particular is able to keep up with her more muscular older brother, as well as her winged friends.

Connection to the Land

I believe this is what allows Applejack to grow plants in crazy places. Not only does the land itself tell a receptive Earth Pony where and when to plant, but what crop to use. Especially well-connected ponies can make plants grow wherever they want, or maybe even whenever they want, considering how many harvest seasons Sweet Apple Acres has.

I have also encountered theories that this same connection is responsible for Pinkie Sense, and thus also Cheesy Sense, so this is the land issuing a sort of warning to Pinkie and Cheese Sandwich, and it was up to them to learn to interpret them -- in which case I wonder how long it took Pinkie to learn that Gummy was in the tub. In any case, this leads to some interesting possibilities in regards to what Earth Ponies can do.

Gearhead and Geomancy

I will take this opportunity to point out that while Gearhead also possesses magic, and learns how to use it, none of it is Earth Pony Magic, and this is why he cannot farm. Gearhead does not possess any Earth Pony Magic, all of his 'slots' being taken up with warped Pegasus and Unicorn Magic. Both are warped enough that it takes a high degree of focus and will to use either of them at all, however the more Gearhead learns, the easier they become to use.

Geomancy is Gearhead's default magic, and it is always active by default, rather than being passive like all other Earth Pony Magic. Gearhead must therefore learn to control his Geomancy, and this is what he spends much of his life doing. Using it to transmute a specific object or area requires a specific and detailed image of the desired result, which also means he must have a good image of what is going on before the change. Given this, he can achieve a high degree of control. While this Geomancy might be similar to Earth Pony Magic in some ways, it is the mixture of his Unicorn and Pegasus magic.

To activate his more standard Unicorn magic Gearhead requires a spell medium like his Geargem Dagger, an activation key, and the full incantation, at least done mentally. Unaided flight is beyond Gearhead as he does not have wings, however he can shape his elemental magic into wings to fly.

Since Gearhead does not possess Earth Pony Magic, he cannot ascend and become an Alicorn.