Sometimes going up means getting on top. No moisture = no chance of ice, that would be one situation where up is better.
If hemmed in by the MEA then up may be the only option.
A rule of thumb (means it is not always correct!) that you will often read is that if you can change altitude by 4000' then you might get out of icing conditions. So if you are less than 3000' abv MEA, climbing might be better because if we believe our RoT, down means you won't get out of it.
".. temperature reduces with altitude. Seems icing would be worse if you climb. "
Colder doesn't mean icing; colder can be better. If you are getting ice at m5C, climbing 4000' to say, m13C can put you outside the icing conditions. Not always away from the visible moisture, just away from where it will stick to you.
All the above is usually predicated on a stable atmosphere, non-convective. Near mountains for eg; all RoT's can go out the window.
Up vs Down: airplanes can always go down. (We haven't left one up there yet!) If you chose down, and it doesn't work out (still icing at mea), what option does that leave you? If you chose up, unless you leave the decision til very late you stand a chance of fixing the problem. If it doesn't work out then you are going down anyway and you will get to 'try' that option.
About moisture and altitude again:
Going higher may not get you into conditions of less moisture, I read that the upper levels of cloud layers have
more moisture.
Not an icing expert; just a regurgitator of readings.
I have read others disagree with going up, too.