Look for the stables outside of the major cities. You can buy them there.

Here's a screenshot of the stable outside of Whiterun:

You can also steal horses (found at stables or in the wild), but there's a 50 gold bounty placed on your head each time a guard is made aware of you mounting one. Stolen horses also run away when dismounted, while owned horses stay where you leave them.

Look for the stables outside of the major cities. You can buy them there.

You can see where the stables are in relation to you (if there are any nearby) by keeping an eye out for the following horseshoe icon in your HUD compass:

They also show up with a similar icon on your map:

And finally, here's what the stables look like when you're in visual range:

You can also steal horses (found at stables or in the wild), but there's a 50 gold bounty placed on your head each time a guard is made aware of you mounting one. Stolen horses also run away when dismounted, while owned horses stay where you leave them.

Look for the stables outside of the major cities. You can buy them there.

Look for the stables outside of the major cities. You can buy them there.

Here's a screenshot of the stable outside of Whiterun:

You can also steal horses (found at stables or in the wild), but there's a 50 gold bounty placed on your head each time a guard is made aware of you mounting one. Stolen horses also run away when dismounted, while owned horses stay where you leave them.