You note that relative humidity is the same outside and inside, which means that you are really asking whether the 10C temperature difference in favour of inside outweighs the fact that humidity inside will increase as linen is drying.
The answer will depend on several other variables: - how much water do you need to evaporate? - how large is the room? - how well is it ventilated? - what is the drying constant of your linen?
Based on the first two, you could calculate an increase of the relative humidity in the absence of ventilation. At 20C, 1% relative humidity corresponds to 0.17 g/m³ of water. So one thing you can do is find out whether there'll be a significant increase in the humidity level of the room.
Then, you're left with many questions to actually get to the dynamics of drying. First, you have to wonder whether the humidity will be homogeneous in the room or not. 414
Experimentally, I can tell you it's not, as my linen dries slower indoors when not spaced enough. [And so, yes, a wind outside speeds up the drying.]
Then also, you have to know how good is your linen at drying, which, to be calculated and not experimentally measured, would include getting to the typical pore size (possibly with two different scales, the weaving scale and the fibre scale). You could also get it experimentally. This would allow you to use <PERSON>'s law to estimate evaporation rate with the different partial pressures outdoors and indoors.
All this being said, with a 10C difference and same relative humidity, I'd dry my linen outdoors. In general, I'd dry linen indoors only when relative humidity is very significantly lower there, or it freezes outside (*), or possibly if I have very little to dry and can spread it well apart.
() ...which turn out to be often both true or both false, as <PERSON> mentions, simply because saturating water pressure increases with temperature, so outside cold air is low in absolute humidity (it has condensated out) and gets also low in relative* humidity when you heat it up indoors. 414