Can I fit 26 x 2.2 tyres to my 26 x 2.25 wheels on my mountain bike? (Not sure of year) 

Specialized Rockhopper
Currently has 26x2.25 tyres, desperately need replacing though,

Mostly used on roads or grass, but trails occasionally 

I'm not a professional, I just like riding my bike
If you want to put 2.2" tires in place of current 2.25" tires, then yes, you can do that.

That's less than a 2mm difference, given that tires conform to marketed width at all (which they tend not to). Generally, any smaller tire size (of compatible beat seat diameter) won't cause any issues, unless there's a huge mismatch between rim and tire width (i.e. 40mm internal width rims and 25mm wide tires aren't a good idea, same goes for 10cm fat tires and 18mm rims, but that's not your case).

I advise to consult this page on a topic of tires sizing.