Air carrier flight crew reported aircraft loss of control during taxi out for takeoff.

Narrative

We were given a clearance to taxi to Runway 13R via Taxiway D; Taxiway C; hold short of C10. We started out single engine taxiing. While taxiing onto Taxiway C; the aircraft slid approximately 20 feet to the left in the vicinity of the intersection of C6. It then began to roll backwards with minimal power of approximately 30 to 35% N1 on the #2 engine. The winds were gusty at the time and the field conditions stated 5 good. In the vicinity of where the incident occurred; the conditions were much worse than 5 good. Once stopped short of the left edge of Taxiway C we opted to start the #1 engine before trying to continue our taxi. Aircraft slid approximately 20 feet while taxiing in the vicinity of taxiway C and C6.We notified Ground of the poor taxiway conditions and opted to have the intersection checked prior to takeoff to ensure that we did not hit any Taxiway lights or if there were any indications of a taxiway departure. We waited for confirmation from Airport Ops; prior to takeoff. Airport operations also visually inspected our aircraft on Taxiway C; short of intersection C10. We did not depart the taxiway. Once the inspections were complete; we departed for ZZZ uneventfully. We were fairly heavy and not taxiing fast at approximately 10 to 12 knots when the event occurred. Our takeoff weight was 157.6.It may have been better to have begun our taxi with both engines running given the wet slippery conditions and the gusty winds at DAL. The taxiways conditions were worse than they appeared and the aircraft slid under the given conditions.