You can add mods during your game. It depends on the mod. There are overhaul mods that require a new game for instance.
You would have to read the mod author pages.
However, It is not recommended that you remove mods during your game. This is a general rule that you should follow. Mods like texture/mesh mods and some item mods can be safely removed.
As Gator posted, It really is a good idea to add them a few at a time and test. I start with things like enb series, texture mods, weather overhauls (make sure my FPS is acceptable). I then move on to major overhaul mods like Skyre.
Test the game after each installation. With the major overhaul mods it is important to ensure they are compatible with eachother. You need to thoroughly read the mod author pages. Proper installation, mod compat patches, bashed patchs,load order,etc are
essential to get a stable game. It's best to stick with only a few overhaul mods. Then I add the extra mods that add items, extra flocks, music, etc. Again it's important to fire up Skyrim and test the mods after you add them.