Couldn't I compensate the high elec. costs with for example cutting heating costs?

The mining rig would then "be the heating body".

Is that doable or should I just go for nicehash?

I pay 25 cents per kwh, therefore mining is not really profitable.
What options do I have, other options like mining with an hdd?

Some people in texas pay 5 cents per kwh so its profitable for them.