An Air Carrier Captain reported they attempted to turn out of their gate after push back and the aircraft slid on ice toward an aircraft parked at an adjacent gate.

Narrative

Light to moderate snowfall on pushback. First off; we were only pushed back far enough to where the deice trucks could apply fluid just off the gate to allow the icing truck to do it's job in the ramp area. Iceman reported ice on high bypass fan blades so they had to deice those (with engines off). For that reason; they wanted us to deice at the gate (just pushed back about 10yards). With the minimal pushback we were very close to gate (minimal turn radius) and an aircraft at our right (unable to turn to the right after start-up). After completing deicing/anti-icing; engine start-up and checklists; our only option was to go right (thankfully no aircraft at that gate); and as doing a tight turn with a completely snow/ice covered ramp (-17C and moderate snow); airplane was sliding straight when trying to turn (after a 90deg turn) and going towards a gate area with a commercial flight on the gate. Recommendation is not allow any type of deicing/anti-icing with ramp area completely snowed/iced without plowing and only allow deicing in the designated deicing blocks.