I've noticed that during wet weather my washing does not want to dry. Is it because of lower temperature, or because of air humidity?
Its because of the higher humidity. Clothes being left out to dry are undergoing two processes: water from the air condensing on the clothes, and water in the clothes evaporating. The lower the humidity, the less water is condensing on clothes and the greater the net transfer of water to the air is.
Temperature plays a role in how fast this process is, but you can have warm weather even when the humidity is high.
You've had good answers already: drying times will decrease as air humidity decreases, and as air temperature increases.
But one extra thought, not covered yet: where you are, do windspeeds tend to be lower when you've got high humidity / wet weather? If the air is warm and dry, but there's no wind, clothes dry slower than if it's colder but there is a wind. So if higher humidity / wet weather correlate with lower winds locally, that would explain some of what you're finding.
[Edit: a bit more explanation:] Unless your house is airtight other than 100% mechanical ventilation, then air currents in your house will vary with windspeeds outside. In the UK, we typically model air-changes per hour as being proportional to external wind speeds (see SAP2009). So, low external wind-speeds will have two effects: they will allow humidity to build up in your house, and they will reduce air convection in the house. Both of these factors will increase drying time. [End edit]