The Elder Scrolls V Skyrim – Where Are Skyrim Screenshots Saved?

It's due to Steam Cloud. It places all saved games in the cloud and loads them when you start the game. If you turn off the cloud in the steam settings then individual windows users can keep their own saved games again.

I'm not sure (only got one gaming PC so can't test), but I guess it has to do with the size of Skyrim savegames (they're rather huge).

I'd suggest - as you probably want an immediate solution - to simply use the old fashioned way: Copy the files yourself.

You don't have to worry about inconsistent cloud states (like overwriting newer saves by accident), because the file names are unique (just make sure to create a new savegame once you've played).

Just copy the savegames you need from your desktop PC to your laptop. You can find the files in the following Folder (just create it, if it doesn't exist):

My Documents > My Games > Skyrim > Saves

The file names should be the same as they are in the game, with an attached .ess file Extension. Pick the savegames you'd like to take with you and copy them to the same Location on your laptop. Once you're back home, do the same in reverse.

Also, you can remove old save games by simply removing them from that directory (e.g. deleting them or moving them to a backup drive with more space).