The first thing most people do in a new browser is type something in the address bar. Horse doesn’t have an address bar at the top, Trails® replace it. Here’s how that works in practice.
To search or type a URL
Open a new Trail: that’s where the search field lives.
Keyboard users: ⌘+T opens a new Trail on your current Trailhead.
Mouse users: Click + at the top of the sidebar

The new Trail opens with a search field. Type a query or paste a URL and hit enter.

From there, every link you click opens a new page on the Trail.
To view or edit a URL
Double-click any page in the sidebar to reveal and edit its URL. Or click ••• next to the page and choose Edit Link.

To copy a URL
Click the page once more to select the URL, then ⌘+C. Or use the Copy Link option from the ••• menu. To copy the URL of the page you’re currently viewing, ⌘+⇧+C.
To change your search engine
Default is Google. Bing, Kagi, DuckDuckGo, Brave, and others are in Settings.
Mouse users: Menu > Horse > Settings
Keyboard users: ⌘+,
And select your preferred search engine from the dropdown menu:

Where the address bar went
Horse doesn’t have a permanent address bar at the top. URLs live in the Trail, attached to the page they belong to. You see them when you reach for them, double-click a page, and otherwise they stay out of the way. Most people stop noticing the absence within a few days. The longer version of this design choice is in where is the address bar in Horse.