Most mounts are purchased with Crowns, not Gold. If you want one, you'll most likely have to paw Crowns to get it. However, the following alternative methods of getting a Mount are available:
Crafting the Pogo Stick mounts from the Five B.O.X.E.S. Event or the School Whirlwind mounts from Aquila.
Certain mounts can be dropped from a select few Bosses around the Spiral. However, this methos is extremely unreliable and a matter of luck.
Some Mounts can also be Fished out of Bundle-exclusive Castles, However, this method is also extremely unreliable.
A select few mounts actually CAN be purchased for Gold. Mostly this is restricted to the Chestnut Pony and the Black Stallion in the Crowns Shop. They're fairly pricey and look somewhat unremarkable, but they do give a speed boost!