There are several possible causes for your problem. If you are willing and able to do some DIY repair work on your car, most can be taken care of at a reasonable cost.
A Mercedes dealership is not usually a good idea. The last training classes on your car were held at a bout the time your car was sold. There are very few of those trained techs at the dealerships now. All too often, you will get the "Yeah, it's expensive - now go away" quote for your car - and even if you do get a straight-up quote, it will still be very expensive at $125 - $175 per hour, plus full Mercedes list price for the parts.
If you are lucky, you might find an independent garage that has SDS (STAR Diagnostic System), the computerized diagnostic/shop manual/test system that is virtually a necessity to maintain and repair your W220. The "indy" can also procure parts more reasonably. While rates vary greatly in different areas, you can usually expect to pay $75 - $150 per hour. - hopefully for the actual hours the shop spends on your car.
I suggest that you start by learning some basics on your Airmatic system. Go here Airmatic - W220 S-Class Encyclopedia
and read thru the article.
If you are willing and able to do some DIY repair work on your car, most common problems can be taken care of at a reasonable cost. You can buy or build SDS for $450 - $650.
One possible cause for your problem is moisture in the Airmatic system. In very cold weather, the moisture can freeze the solenoid valves in the Valve Block that the control system uses to distribute the compressed air that operates the suspension. You can make (or possibly buy) an in-line filter that contains dessicant to dry the air.
Another possibility, as already mentioned, is that the piston in the Airmatic Compressor is worn. You can buy a kit to rebuild the compressor very reasonably ($25 - $50), and installation isn't difficult.
While leaking struts are a common problem, it is very unlikely that all four struts have simultaneously failed. Used struts can cost $150 - $250 on eBay, Cheap Chinese struts (NOT recommended!) about the same, Arnott rebuilt (life-time warranty, recommended) $360 - $375, Bilstein new (recommended) $825 - $850, Mercedes rebuilt $1000 - $1200. All of these are estimates for single struts.
I do my own maintenance and repairs, and would never consider going to conventional suspension. YMMV.
Here is an article on on the subject - I don't know how old it is. S-Class W220 Aftermarket Air Suspension Struts and Conversion Kits – MB Medic
You can find numerous threads and videos on the subject.
A final opinion...
Driving a W220 is a joy, and can be affordable if you are able and willing to do most, if not all, of the necessary maintenance and repairs. If you are willing to pay an independent shop to do all necessary maintenance and repairs, it will be expensive. If you can find a dealer who will work on your W220, it will be VERY expensive.