My first recommendation is to get a multimeter, if you don't already have one, and check the voltage on those wires coming off the fan when the fan is running. LEDs have an operating voltage. That is, when an LED is lit, there will be a particular voltage drop across the LED. The exact value depends on the details on how the LED is made, but a typical white LED will be around 3 volts. If you put a white LED in parallel with a fan, and the fan needs 5 volts to operate, the LED will end up clamping the voltage to 3 volts, and the fan won't run. (The LED will also run pretty hard and won't last long.)

One important thing... are these inflatables battery operated or powered off the mains? If off the mains be SUPER careful about the wires when you check the voltage. Treat them as if they could be live. While the voltage might be 5 volts, you don't know if there is proper protection on that, and you could get a nasty shock off them. Don't touch the wires while the thing is plugged in, and don't let them come in contact with each other or anything conductive.

So, check the voltage across the fan and see what it's running at. I'd guess it's running at 5 or 6 volts or possibly 12. If it's 5 volts, put a resistor (100 ohm 1/4 watt should be fine) in series with the LED and the two of them together across the wires:

WIRE----RESISTOR---LED---WIRE

If it's 6 volts, you can do two LEDs in series (maybe with a small resistor in series as well):

WIRE---LED---LED---WIRE

If it's 12 volts, you can try four in series. Make sure the LEDs are wired in the same way, since they're polarized.

Another possibility is to get LED tape. You can probably find LED tape that will match the voltage of the leads without much fuss.

Finally, you can order resistors online. I don't know what country you're in, but in the U.S. you can order resistors from various places: Adafruit, Digikey, Mouser. You can even get starter kits that have various resistors in them.

EDIT: After I posted this, I got to worrying about my response. Frankly, if these things are powered off the mains, I wouldn't recommend messing with them. It isn't just the shock risk while you're working on them, it's the risk of a short and/or fire while they're operating at night. They'll be outside, where they could get damp and so on. That's really not a serious problem for something that works off batteries, but for something that's mains powered, it could turn bad. You want to be sure of what you're doing before messing with something like that.