If you have an instrument rating, you may legally fly an approach to whatever the minima are for that approach. It will vary depending on the approach type, and even for a specific approach type the minima will depend on the specific airport in question (e.g. high terrain nearby might increase the minima).
As a guide, the very lowest you could expect would be a 200' decision height (the height by which you must be able to see the ground) for a precision approach.
That's the legal side (very simplified). But there are practical considerations, too. You say you are flying a single-engined aircraft. If you carried out a flight of any length with a 200' cloudbase and experienced an engine failure, you would not get to see the ground until a few seconds before you hit it - it doesn't give you very much time to find somewhere for a forced landing. A cloudbase of 1000' might be considered a sensible minimum for any extended period in a single-engined aircraft, although this will depend on your personal view of the risk involved.
The other thing to bear in mind is currency. To be able to safely fly an instrument approach to 200', you would need to be extremely current. Many pilots who do not fly commercially would not be able to fly instrument approaches regularly enough to be able to do this safely.
Finally, there are icing considerations to consider. In an aircraft with no anti-icing or de-icing, you may not fly in known icing conditions. That rules out any flight in clouds or precipitation where the outside air temperature is freezing or below.
I'm sure there are more considerations, too, but I think I've covered the main ones.
FFF
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