Lets say I want to make a VLF loop antenna for a Sub AM radio band. I don't want a full wavelength because that would be a humongous antenna. Would I wind more turns of wire to decrease the frequency it can operate on, or is there any other way without a phisically enormous loop?
There are plenty of ways to make antennas smaller. Unfortunately, all of these things also make the antenna less efficient. Economics provides a compelling proof: if efficient, small, low-frequency antennas could be realized, why do AM broadcast stations erect huge, expensive towers to support their enormous antennas?
Antenna inefficiency isn't necessarily a problem for receiving, as long as the received power is enough to overcome your receiver's noise floor. See What is the relationship between SWR and receive performance?
For transmitting, an inefficient antenna can still work, but it's much more difficult to come up extra transmitter power, and find a way to handle all that heat. A longer wire is usually cheaper than a 10kW amplifier.
To your specific case: the type of antenna you are describing is a small loop antenna. These antennas are not resonant, by definition. When resonant operation is desired, a capacitor is added at the feedpoint to create an LC resonant circuit which greatly increases sensitivity at the resonant frequency, and greatly decreases bandwidth. Since the small loop is an inductor, adding more turns increases the inductance, and thus lowers the resonant frequency if the capacitor is not changed. Increasing the permeability of the material inside the loop also increases the inductance.
If you think a lot of turns around some high permeability core is a good idea, you have conceived a loopstick antenna:
However, such an antenna will not work well for transmitting. The ferrite will saturate at very low transmit powers, and the ohmic losses of the many turns of wire at any reasonable transmit power will make it a better heater than an antenna.
If you're going to be using this antenna strictly for reception, then increasing the windings is fine, but as the previous answer stated you're on increasing inductance, and when you increase inductance, you are by nature adding more radiation resistance. So, for transmitting that is not ideal at the wavelengths of VLF. These are small loops and can only radiate a small amount of the power from the transmitter. So increasing the windings will get you properly tuned for reception (i.e. the small magnetic loop in AM radios), but not very effective for transmitting.