Applejack chastising Twilight for using magic in the episode "Winter Wrap-up" was because she supposed to be wrapping up winter "...the earth pony way". (You know, like how Twilight sang in the song "Winter Wrap-up"?). Since earth ponies don't use unicorn magic, it wasn't allowed to be used for wrapping up winter ANYWHERE in Ponyville, not just Applejack's farm. This is further evidenced by no other unicorn(except for Rarity who apparently thinks she's special...) using magic during the wrap-up. There have been plenty of times where Twilight has used magic on her farm during the episodes "Applebuck Season", "Return of Harmony" Pt. 1, and "Super Speedy Cider Squeezy 6000" wherein Applejack didn't get angry or frustrated at Twilight for using magic. To that end you've analysed Applejack's line incorrectly.
She was disguised as a tree in one of the episodes so whatever species that one is.
Because magic makes it all complete? *ponyshrugs*
Remember that point in "Mare In The Moon" pt 2 where Nightmare Moon tried to destroy them but failed? That proved once and for all that it isn't possible. The elements are physical manifestations of the virtues they are linked to, with magic being represented by friendship in and of itself. That's why the show is subtitled "Friendship is Magic", litterally it is the essence of friendship(in it's various forms) is a source of immense magical energy. Other examples that aren't the elements themselves are seen in "Hearth's Warming Eve" and "A Canterlot Wedding" pt. 2 wherein interpersonal bonds power immensely powerful magical spells.
tl;dr not possible, it's been tried and it didn't work. You would have to destroy friendship and virtue itself.