Depends on what kinds of "mods" you mean. Generally, in NWN lingo, "mod" means module, i.e. user made custom adventure, either multi- or single-player. Normally, only the host needs the module file, but if you added any custom content through hakpacks, the players need those too.

So the question is if you made any changes, and if so which kinds. Roughly, I'd say there are 3 kinds of situations to consider:

1] Purely Visual Mods that replace existing stuff.

Say, you install an override to make undead look cooler. (There is one. It's pretty nice.) These kinds of overrides usually don't cause any conflicts: if you install the Cool Undead (tm) and your mate Bob doesn't, then all that happens is you see a scary looking zombie on your screen whilst Bob sees a normal looking zombie on his.

The only issue is if you use something like custom head overrides (which also exist) that add extra heads on top of the normal ones. (instead of replacing the normal ones.) If normal heads go from head number 1 through head number 15, and you have head number 22 and Bob doesn't have the head-override installed, then to Bob it will look as if your character has no head at all. (Just a neck-stump.) The game won't crash or anything, but it's annoying for Bob.

2] Simple script changes

These depend on the server host and whatever module he's running. If you set up the Goblin Hunt adventure and want to make it so the Magic Missile spell kills Goblins instantly, you can change the script in my module to make it do that. I on't have to do or download anything: as soon as I join your Goblin Hunt server, my magic missile spells will blow up Goblins.

You could also make it so that Barbarians get 20 hitpoints per level on my module. This won't work if the module uses the local-vault (People can bring in their own characters from other modules) but will work fine if your multi-player module is server-vault. (everyone has to create a new character which is stored on your PC, not theirs.) Again, no need to download anything.

3] Anything involving new visuals or more complicated changes.

If you want to play a module set in an Elven Tree City, both the players and the module host will have to download and install the Elven Tree City hak, because there is no Elven Tree City in the default game. Same for items with non-default appearances. Same for more complicated changes to characters like new classes, races, etc. You need to download the right haks to play the module, whether you want to play it single- or multiplayer.

For example, many modules require the CEP, which adds tons of new visuals. Everyone who wants to play such modules has to download the CEP, no ifs and buts about it.

If you want to play the official campaigns with a friend, your friend normally won't need to download anything at all, unless you added hakpacks to the campaign modules or something.

The OC and Shadows of Udrentide are set up to accommodate multiplayer, but Hordes of the Underdark isn't. It has some strange things with cutscenes that may or may not work.