I have half a pilot's license. My checkride was yesterday at Castle. I did great on the oral exam but decided to postpone the flying portion because the winds got too strong (17-25kts). Same thing forecast today, so now I'm in limbo hoping to finish the exam next week. Grr! calculate wind corrections. Easy when travelling straight, but one of the checkride tests is flying a perfect circle around a landmark. Not easy with a 20kt wind blowing you off course.
Steady winds straight down the runway present no problem, if anything they make it easier to takeoff and land. Winds blowing across the runway are a different matter; difficult crosswind landings are something every pilot respects. Coming home yesterday I landed in a 10-14kt crosswind at San Carlos, but it took me 3 tries.
The biggest problem with strong winds is they're seldom steady. If a wind is 10kt gusting 20kt, your airspeed may suddenly drop 10kts in a lull. That can be a problem if you're flying slow near stalling speed. And gusty winds require active flying to stay pointed the right way. San Carlos has a bunch of mechanical turbulence from the wind swirling around the buildings near the runway. Crosswinds there don't just mean a static correction, you have to sit up and dance fast on the controls like you're playing a videogame. It's kind of fun but very demanding.