Various sources indicate that when climbing to slide back on the saddle. In about a month I plan to attempt Whiteface Mountain with its 13 km at an 8% grade. If I manage this climb I will be at my limit. Should I move my saddle back for the climb?
Most of the new schools of thought suggest moving back or forth on your saddle is more of an indication that the saddle offset isn't set up correctly, than it is advantageous. I would tend to agree. If you find yourself constantly shifting forward or backwards, this likely indicates that the saddle isn't in the correct position.
Old school fitting have been obsessed with KOPS (Knee over pedal spindle), but this was originally derived as a general method to determine whether or not a frame size was appropriate (i.e., if you couldn't get into KOPS, you needed a different size). (There isn't even consensus on how you even measure KOPS as everyone landmarks the knee differnently - this can result in over 1cm difference in offset alone). Depending on your body proportions and bike position if you setup your bike to comply with KOPS this may have put you into a sub-optimal position, which is why you may find yourself moving forward or backwards.
Best advice is to go out with a set of allen keys and level and ride a reasonably long climb. If you find your self wanting to move forward, try moving the saddle forward (0.5cm at a time) then retry. Eventually you should be able to fine tune your fit. The level is used to ensure you can keep the attitude of your saddle (i.e, nose up, level, or down) the same between trials. Optimal saddle attitude is a topic onto itself (I feel a lot of "experts" have little understanding on the functional bio-mechanics of hips and how this inter-plays with saddle attitude.)
In about a month I plan to attempt Whiteface Mountain with its 13 km at an 8% grade. If I manage this climb I will be at my limit. Should I move my saddle back for the climb?
Honestly, I think gearing will be the most important factor for surviving 13 km at 8%. I have done a 40 km ride at a similar gradient and being able to spin is a life saver (when I saw the "only" 19 km remaining I shed a tear). There are lots of long cage road derailleurs and wide range cassettes available now. I would consider this as the most important change over fine tuning such as saddle offset.
It is not necessary to change your saddle position for climbing. It will not increase your chances to overtake this mountain. It will only give you a less confident feeling as you are riding in a position you are not custom to.
I recommend to do this at the most comfortable position you know and that is your current saddle position.
If you can, try and stay in the saddle, going in and out the saddle costs energy. I only recommend going out the saddle when you feel the current section you are on is too steep ( but you must feel this for your own ) or you feel you should change the tension on the muscles ( climbing is a constant tension for the muscle and to change the feeling you can go in and out the saddle ).
As for you being at the limit. I don't think that this is possible, almost anyone can do these climbs if you have the right gears to do it and the motivation to get to the top!
Moving backwards in the saddle straightens out the leg and increases the peak power output (hence why track sprinters have their saddles set so high), but it also reduces efficiency.
The advice to slide backwards in the saddle was probably meant for short steep sections.
Think about getting a gear ratio that lets you pedal at a reasonable speed and sit in as normal a position as you can as this will be the most efficient and effective.
Depends on whether road biking or mountain biking. in mountain biking you are looking for traction on uneven terrain when climbing - sitting forward facilitates traction on both tires. In road biking, you have smooth tires and smooth terrain. Shifting slightly back in saddle when climbing increases traction on the rear wheel, which is the only wheel taking your power (front wheel is passive), and reduces friction on the front tire, which is what you want.