Not to put down cold start valves, but in over twenty-five years working around mostly MB German cars, I have seen maybe three cold start valves causing problems. All of those were leaks and had nothing to do with cold starting.
But I do live in Florida. Cold start valves don't operate ever above 59 deg F. so cold is relative. A cold motor does not necessarily ever see cold start valve operation. In Florida it may never see cold start valve operation.
Its very likely that the valve plays a big part when real cold, I can't say, but usually cold start problems are due to other system weaknesses. Poor plugs, bad mixtures, weak wires. Testing always is the answer.
Bosch Master, ASE Master, L1
33 years MB technician