A large range of arduino-compatible temperature, humidity sensors are available. For example, a list of sensors is available here.
I tended to use a BME280 in the field which also measures air pressure in order to estimate piezometric level (see my post on water pressure sensor). Don't forget to also use a radiation shield to protect the sensor from rain and solar radiation (for accurate temperature measurement). You can find relatively cheap shields, such as this one from Seeeduino. Even better, you can 3D print it, here is a very cool tutorial with 3D plans, I tried it, it works nicely !
One note of caution, although the air pressure and temperature sensor measurements appeared to be very satisfying, with a similar precision as commercial sensors, the relative air humidity measurement seems less accurate. Indeed, when air moisture is high, the measurement seems saturated and remains stuck at 100 % and only decreases when a significantly drier weather occurs. There may be better outdoor sensors for air humidity.