A cartoony-character would remain more or less the same, but they'd have no particularly special abilities. Your character, for instance, would have all the normal abilities of a pony who somehow has wings. (It's your call whether her wings are capable of achieving lift without any special powers.) But otherwise, yeah, she wouldn't be able to achieve anymore speed than a normal pony could.

Besides that, the Shift in the tunnel won't kill anyone or outright disable them. So a being who relies on magic would still be able to survive in the tunnels, even though they technically shouldn't be able to. (The field generated by Shifters works in the same way, incidentally.)