Fractional jet Captain landing at a non-towered airport reported failure of thrust reversers on an icy and snowy runway resulted in a temporary loss of control.

Narrative

Night landing at ZZZ with two crew; one passenger. Runway was snow covered (approximately 2 inches) with ice layer underneath. All NOTAMs; weather; and pertinent info was checked prior to departure. Verified by automated weather system before landing. No NOTAMs or other information was posted or broadcast warning of the unsafe runway conditions. Company dispatch called on telephone to schedule an arrival with after- hours service of fuel and handling; and no mention of unsafe runway. The runway is 5;000 ft long. Smooth; stable approach was conducted with full flaps and airspeed was maintained at vref just prior to touchdown. Normal 3 degree approach angle; and normal touchdown near the beginning of the runway. Upon touchdown; speed brakes were extended; and thrust reverser levers were pulled. The right thrust reverser would not deploy with attempts from both pilots (different pressure; wiggling the lever; etc.) Anti lock brake system was working; but on an icy and snowy runway we had very minimal braking effect. Approximately 3;000 ft down the runway we were finally able to get both of the thrust reversers operational. Maximum thrust reverse was applied; along with continuous maximum braking. The aircraft came to rest/control approximately 100ft or less from the end of the runway. We stayed on the runway at all times; but nearly didn't stop in time. We slid left and right and drifted down the runway almost the entire time. The airport should have been plowed and cleared. We were told by an employee that 'It has been like this for a few days.' And that 'Someone should plow it sometime.'. If the airport had a NOTAM reporting such dangerous conditions; we as a crew would not have flown to this airport and elected to go to a clear runway with safer conditions. Contributing factor to the dangerous situation is the lack of equipment (thrust reverser) working properly.