When planning your trip check the DEC website to see what trails are open. Some trails may be closed due to mud, high water levels which have lead to flooding, or washing out trails completely. I've seen some trails closed due to damage winter storms have caused as well. I remember one year DK and I had to climb over these huge trees that blocked a trail one spring.
Also keep an eye on the weather conditions as they are more apt to change quickly during the Spring, especially at high altitudes. This means you could suddenly go from sunshine to a snow storm in the blink of an eye. So if the weather guy says beware, maybe postpone until a nicer day.
Make sure you have proper gear and clothing. This is one of those things that really tend to depend on several factors, eg. how long you will be gone, where your trail is located, and your own personal factors.
Here are a few things you should carry no matter what season you're hiking in.
Map: a topographic map is probably
Compass: make sure you know how to use it
Flashlight / HeadlampExtra Food and water
Firestarter: of any kind matches, a lighter, fire striker
Insect repellant: It's good to have on hand since you never know when those little buggers will be out.
Sunburn protection: because you can get a sunburn even on a cloudy day.
Extra Clothing: I would highly suggest you have extra clothes when hiking in the Spring. Personally after a few rookie mishaps I now keep an extra set of shoes, socks and pants in the car.
When getting dressed layers are your friend. Spring days usually start out fairly chilly and then warm up, not to mention once you get moving you'll warm up too. I like to start off with a light jacket over either a longsleeved or regular tee-shirt. Personally I've found that nylon workout capris work best for me, but you can go with light pants if it's early in the season or shorts if it's later in the season. If it's early in the season you could also pack a pair of light gloves and a hat or headband.
As there is the possibility of runoff from melting snow, and high water levels from Spring showers, a waterproof pair of boots would be a good idea.
A big thing with spring hiking is to not get to wet given the cooler temps it could lead to hypothermia, yet may also lead to pleasant hiking experience without sweltering heat or bugs. Hiking in the spring can be an enjoyable experience, as you can see things like this, but play it safe and make sure you have the proper gear.