I suspect that budgetary aspects have also restricted some of the more fantastic elements being realised onscreen.
I personally think that the truth is somewhere between DalekJim
and 137th Geibirg's
respective positions: the series makers did, for the most part, dial down the fantasy elements in S1 so as to appeal to a mainstream audience. They did have the white Walkers in the pilot episode but, until the dragons appeared, the magic was largely excluded (exorcised if you prefer, ho ho ho) until the mainstream audience, who might otherwise have turned off, was totally hooked.
There is definitely less magic or fantasy in the tv version than in the book, but you still have Melisandre's Smoke Cloud (good to see him getting work after Lost ended), said dragons, a resurrected man, Bran's warging and visions, the walkers, giants etc.