Sort of depends on what kind of antenna, and…
First of all, put your fears to rest because a properly installed, maintained, and grounded antenna will not short out in the rain. It also won’t pose a risk from lightning. However, an older amplified antenna could very conceivably short out.
An antenna is a way to conduct electricity; that’s its very reason for existing, because radio waves are nothing more than electromagnetic energy at a very weak level. A regular antenna does conduct that electricity but it doesn’t carry a current of its own, therefore there is nothing in the antenna itself to short out. However, every antenna made today has a balun which converts the impedance of the signal from 300 ohms to 75 ohms so it can travel efficiently through coaxial cable. This balun is generally a weatherproof part, but if it gets old it can get exposed to the elements. Look for a plastic box near where the cable connects to the antenna. You should be able to look at it and determine if water has the ability to get at electronic components.
In the case of an amplified antenna, there is power coming up the cable and into an amplifier built-in or placed near the antenna. Again, these devices are intended to be weatherproof, but time, water and UV rays can weaken the plastic outer coverings. Your amplifier does have the potential for shorting out in the rain and should be inspected every year along with anything else you have outside.
If you have a rotator, there is definitely a potential for a short circuit if the plastic housing is cracked or in poor condition. Rotators are simply high-strength electric motors and there is a real possibility that water getting where it shouldn’t will shorten their lives considerably. You should make sure there’s no possibility that water could get into the rotator mechanism or even pool anywhere around it.
It doesn’t take a lot to inspect an antenna or its accessories for signs of wear. You’re looking for cracks or loose spots, places where water could get in. It’s also a good idea to rub your finger briskly against any plastic parts to see if they are oxidizing or turning to powder. This is a common occurrence in the southwest. If you see signs of mold, which is more common in the southeast, that’s a sure sign that there’s enough water to create problems, but don’t confuse the black oxide finish that forms on aluminum antennas with mold. The oxidation of an antenna doesn’t have any negative effect on its efficiency.