So I'm a ps3 guy but had to get Morrowind to play it. My question is, can I play it on my laptop?

Generally - yes. Can we have your laptop's specs?

I'm not home. Just was curious if it could be done or if you needed a desktop.

Not really. You would need a fairly powefull desktop to run Morrowind with latest graphic replacers and mods etc. but you won't need one if you have a fairly recent laptop and just want to play vanilla Morrowind.

It doesn't matter if it's a laptop or desktop. Specifications matter.

Any typical laptop you could buy from Walmart in the last few years should run Morrowind without any trouble at all.

How could one possibly be an "Elder Scrolls veteran" but new to Morrowind?

(unless that person has indeed been playing Arena and Daggerfall back in the 90's but somehow skipped playing Morrowind and jumped into Oblivion...)

EDIT: Regarding the original question - as long as your laptop has a dedicated GPU, it should be good! I can't imagine it'll run well if the laptop has only an integrated graphics chipset though...

It will probably run fine if you have a recent laptop. I have one from 2010, I think. It runs Morrowind fine despite having Windows 7 as the OS. Be sure to download Morrowind Code Patch and Morrowind FPS Optimizer if you want the game to perform better. Using the Code Patch just fixes a good amount of noticable bugs like the one where you have to wear armor to get unarmored experience. Just look around the mod related stuff section on the UESPWiki page for Morrowind.

Well, even Oblivion has been around 6 years now; that probably counts as veteran for a lot of people.

I can run Morrowind fine on my dads terrible desktop with a terrible integrated graphics card so yeah you'll be okay as long as your computer is fairly recent.

Vanilla MW should run fine on anything built recently. Many of the graphics mods will be a problem if you don't have a decent GPU, which most laptops don't.

I run it on four years old laptop with an Intel Core 2 Duo @ 2.4 GHz and an ATI Mobility Radeon X1350 with Windows 7. It runs Morrowind just fine at highish settings (without graphic replacements, though) and even runs Oblivion using low settings.