not only will you likely have the trail entirely to yourself, but you will also enjoy; cooler temperatures, a refreshing mist, a chorus of raindrops falling on the leaves, your boots going squelcho mode, the fog rolling in as the rain recedes, being snug as a bug in your warm clothes, and so much more!
just make sure that you plan accordingly and that your gear is actually water-PROOF not just water-RESISTANT (learned this the hard way), that the rain won’t develop into a thunderstorm and that you aren’t in a flood prone area, and that you’ll have dry clothes at the end of your hike to change into and some trail mix and jerky to snack on.