Why doesnt a field coil in a DC shunt motor lead to short ciruit when it is a fact that an INDUCTOR is a short circuit to DC?

Yes, an inductor is a short circuit to dc...that's true....IF the inductor is an ideal one, that is, the inductor has no resistance but has inductance only. Anything in real world, as you know, is not ideal. An inductor is usually made of a copper wire. A copper wire has its own resistance. If an inductor coil is thin and long (i.e. many turns), it will provide an appreciable resistance to DC, and will no longer be a short circuit.