If a plane lands vertically in a strong headwind, what will the pilot do to exit the runway? If he increases the speed, wouldn't that be dangerous (I mean he will fly again)?
If you're in a situation where you can "land vertically" (I assume that means you are landing into a headwind equal in velocity to your landing airspeed), then it's simply dangerous for an aircraft to be anywhere on the ground without being properly tied down. Even if you were able to turn the aircraft, it would probably be lifted into the air again as the wind caught the fuselage broadside.
I landed a C-152 at KMHV (Mojave, CA) with AWOS saying winds were 38kt gusting to 45kt straight down runway 8. It was not a vertical landing but the ground effect lowered the landing ground speed to ~15kts. Why? Because the pilot side door opened in moderate turbulence at 7500 MSL and would not latch, and was banging in the turbulence and freezing my head since OAT was ~10F. (Hard to fly the plane while holding the door closed!) I taxied very slowly with the controls in the 'keep-it-from-flying' orientation, parked facing the wind, bent the door frame back by hand to get the door to latch, taxied back to 8 very slowly, advanced the throttle and departed with a 100 ft roll.
EDIT: 20180405 ...
I just look at the control surfaces to make sure they are forcing the plane DOWN given the direction the wind coming from... Here is a better description:
From the AOPA Windy Flights Page
Taxiing in a crosswind requires additional control inputs to keep the airplane's tires well planted and, in a strong crosswind, to prevent a wing or the tail of the airplane from being lifted by the wind. It can be confusing remembering which way the ailerons should be positioned during a crosswind taxi, but this memory aid may help: When you hold the yoke, your thumb points up; when the wind is coming from in front and to one side (a quartering headwind), point your thumbs into the wind. When the wind is coming from behind, point your thumb away from the wind. So, for instance, if the wind is coming from the left rear ( quartering tailwind), deflect the yoke to the right (thumb points right and away from the wind).
To remember the elevator inputs during a crosswind taxi, remember that when taxiing downwind (in the same direction as the wind is blowing), the elevator should be down. When taxiing upwind, the elevator should be neutral (for tricycle gear airplanes) or up (for tailwheel airplanes). Watch the movement of wind socks, flags, grass, etc., as you taxi, and change control inputs appropriately as your taxi direction changes.