It could cause you to have to crank longer on cold starts, although similar conditions on warm start would be less abnormal and more likely to be a fuel supply problem.

See if you read line voltage from the wiring harness to the cold start injector, when the car has sat overnight in cool weather (like now).

If the signal exists, the cold start valve is faulty. The cold start valve adds more fuel to the start and cold run mixture for better performance when starting and first started. Then it shuts off.

By the way, don't let "cold start valve" and "cold start injector" fool you. They are the same thing. It's another issue of semantics, like "air mass meter" "air flow meter", and "mass airflow sensor".
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1992 940 wagon, 72k
make people envious; smile often.