You are just going to have to print samples. Many things will change the diameter - most importantly how far the pin is above the heated bed as temperature drops as you get farther from the hot glass.
Some points.
1) In general for pins you should get what you ask for. Unlike vertical holes. Because your pins are 100% filled, there's no where for the filament to go.
2) If you print a single pin it won't have much ability to cool down so you should always print at least two so that one can cool for a few seconds while it prints the other.
3) Unlike PLA, Nylon is likely to have bad layer adhesion so the pin may be quite weak if printed vertically. This should not stop you from printing vertically. Instead you should enclose the printer (throw a sheet over it) to try to get the air temp up to maybe 30 or 35C. Also lower the fan as low as possible but where it is around 1/4 the volume of full speed. Typically 3% for an S5 (or 6% for Um3 or 30% for UM2 - every model and even different versions of the same model will be different on this).
4) Break a few pins. On purpose. Print some extras. If they break along layer lines your adhesion is probably not good enough (need to lower fan some more or raise air temp some more or both).
I would not print horizontally but that will certainly give you the strongest possible pin but will require lots of PVA potentially.
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