I believe that the right mindset in life will allow you to do almost anything you want. Often those with a great mindset will do well in a variety of fields. Finding a balance between being determined to push yourself, knowing when it is appropriate to do so, being critical when things don't go to plan and all while keeping positive and realistic is the key to a good mountaineering mindset.
Most winter climbers in the UK probably climb comfortably below their physical limit and this is for good reason. Leaving a safety margin is vital to move quickly, efficiently and allow room to adjust if things go wrong. Simply getting on intimidating routes in the first place can be the crux. However, before doing this, it is important to have a good understanding of conditions and gear first. This way, when you do push the boat out you are still in control and a fall isn't going to be dangerous. You should have a solid understanding of your ability and the terrain that you're on to calculate when it's appropriate to try hard. Not all routes have gear everywhere you want and so not all routes are ideal to push your grade on.
In the mountains I found I made bigger advances in my progress when I changed my approach rather than any physical training. Controlling the limiting factors is vital to squeeze out every possible advantage. I have written a full article on the tactics that I use winter climbing which can be found here.
Failure is a huge part of the game in climbing. In a sport where consequences are high for making mistakes people should not ignore signs to turn back. Bailing off a route just meters away from a summit can happen and adopting an accepting attitude towards this will make it easier. Being too headstrong can get you into trouble.
As you get older you build up a bank of experience and this makes your movements and decision making much more efficient. This will result in a higher success rate. Poor decisions will far supersede a lack of physical ability when it comes to reasons that people fail on an objective in the mountains. In winter climbing or on big peaks taking a patient and steady approach will allow that experience to be built up over time. Don't jump grades, make sure you are consolidated at a particular grade before moving on. On alpine peaks it can take years for the stars to align with climbing partners, conditions and fitness, so patience is key. At the same time have a sense for when the time is right to push on and don't stagnate at a grade because you believe it is your limit.
To speed up the learning process it is vital to have a critical mindset, this will allow you to identify weaknesses, improve faster and build up that experience that is required for success. With that said, don't be hard on yourself for failing, if there is a reason, change it next time and stay positive. Being negative will also reflect on your performance.