If you put your mountain bike away during the cold months, then it's time to get it out and look it over. You never want to take your bike from storage and hit the trails immediately. This is potentially a disaster. It can harm your bike, and more importantly, yourself. Mountain biking is a bit different animal than regular cycling. You're putting harsh miles on your bike. You need to make sure that everything is in tip-top shape before you hit the trails again.
Here are the main problems to look for. If there are issues, then head to your local bike shop and get them taken care of.
The tires need to be thoroughly inspected. Even if they have air in them, that doesn't mean that they are in good condition. All that means is that there is not a serious leak. The inner tube might be in terrible condition and ready to explode. Mountain bikes get lots of mud, water, and dirt in the tires. These all can wear out the material. If any of that debris gets inside the wheel walls, it will damage the inner tube. You should have your inner tube inspected. They are not expensive to replace and it is much easier to have them replaced at a bike shop while the bike is up on a stand than out on the trail with only emergency tools.
Some people think that the only thing they have to do for a bike chain is oil it. Well, not mountain bikes. Mountain bikers fall, crash, and put their bikes through much more wear and tear than regular riders. Because of this, the chain can become damaged. If the gear cannot engage the chain correctly you won't get a smooth ride. You might be able to pedal, but you risk the gear catching the chain at the wrong angle. That can destroy the gear and send you flying.
It is very important to check the brakes. This includes the brake pads, as well as the brake lines. Brake pads wear down very quickly during tough rides. If you didn't check the lines before you put the bike away for the winter, then you must inspect them. This means checking the connections at the handle, as well as at the pads. The cables must be taught and not frayed. If the pads look dried out and cracked, then you need to head to the bike shop and have them replaced.
The most serious problem might be the one you don't notice. The derailleur is a big issue for mountain bikers. Every time you hit a hill and take a fall, you put your derailleur at risk. If it bends or warps, then you are in for a world of trouble. The derailleur is responsible for switching gears. If you can't move from 2nd gear to 8th gear, then you might end up walking your bike up that hill.