Dorico approaches shared staves in a slightly different way to some other programs.
The idea of Condensing is that you have four entirely separate Horn players, each showing a stave, you write whatever you want into the four individual staves, and then before printing the score you go Edit > Condensing and Dorico automagically combines the contents of those four staves onto fewer staves in the score. As you’d already started with four separate staves for four separate players, the parts are easy - they’re generated like any other part, with Horn 1 on one part, Horn 2 on another part and so on.
(As to why Dorico handles condensing this way, with separate staves that are combined rather than a single stave that is automagically “split out”, it’s to ensure that the parts consistently reflect exactly what you’d intended. As a newcomer to Condensing it may seem like a slower approach to start with individual staves rather than writing straight into combined staves, but Dorico makes it easy to input notes into multiple staves simultaneously and if that doesn’t suit you can rapidly explode music to multiple staves.)
In order to tell Dorico you consistently want Condensing to put Horns 1 and 3 on one staff and Horns 2 and 4 on another, go to Layout Options > Players > Condensing - for the score layout - and set a Custom Condensing Group that contains Horns 1 and 3 and another Custom Condensing Group that contains Horns 2 and 4. Then when you turn on Condensing (on the Edit menu, or at the top of Layout Options > Players > Condensing) Dorico will respect those Custom Condensing Groups.
If you disagree with the way that Dorico displays your condensed material in the score, go to Notation Options > Condensing and have a good look through the settings there. They can also be overridden on a local basis by way of Engrave > Condensing Change (only available in Engrave mode), but this typically isn’t necessary.
Then for the parts, I must admit I’m a little hazy about what you want. In the session world here in the U.K. each horn player has their own music stand, but sometimes we give two or four (or heck, 12!) players the same page of music.
For instance, if you want Horns 1 and 2 on a single part, select the Horn 1 part in the right panel of Setup mode and tick the Horn 2 in the left panel of Setup mode. Then select the Horn 3 part in the right panel and tick Horn 4 in the left panel. Then delete the redundant Horn 2 and Horn 4 parts from the right panel. If you actually want to display Horns 1 and 2 on a single stave in a single part, you can do that too, by turning on Condensing for the Part layout. And if you want all four staves on a single part, you can do that via the same method, with or without Condensing turned on (and probably with empty staves hidden from the Staff Visibility section within Layout Options > Vertical Spacing.