125s do not like heated grips. Oxford do some designed for low powered bikes which might be suitable.
The problem is that the batteries are often so small and the generators don't provide the output required to charge and power the grips.
Hand guards are good if you have sound winter gloves and get big enough ones. As you say, it eliminates the wind blast. Personally, I use the combo of hand guards and heated grips. I find hand guards to be good on their own and you can get them for £30 (acerbic storm) but they must be well positioned and also wrap around enough to block all of the wind. Really, I've only seen the ones that are about £100 do this properly and they needed extra deflectors as well at about £20 each.
If you were to just have one option then it'd be bar muffs as they keep your hands warm, dry and don't require any electricity. You can get the oxford ones and upgrade them later as they have pockets in them for oxford's over grips. These normally slip over the normal grip (longevity is apparently crap as they fall apart) but they open out into a flat pad and go inside the muffs to warm them up.
Personally if I were in your position, I'd just shove the muffs on there. Spending £70 on a 125 that you're not going to keep for too long is a little daft really and it also potentially reduces the value if you screw it up.... like I did. Muffs are about £30, cover all of your hand and will keep you warm.
There are a couple of downsides to muffs:
they're not for the fashion conscious
they can get in the way of switches, etc and must be carefully fitted to avoid this
there's always that sensation that they might trap your hands if you were to have an accident which would cause you to do a superman over the front, with obvious consequences. Whether this would happen in practice, I dunno.
Summarise: grips - expensive and potentially not suited to a 125s generator output. Hand guards - need to ensure they completely cover your hands, expensive for good ones. Muffs, better all round bang for buck but look meh and can get in the way.