/ winter fitness
Is it long walks / steep hills with a heavy pack or running?
For ice axe stamina improvement will sessions at the bouldering wall be beneficial?
Not sure why you ask this from your profile info. Here's a genuine answer, not meant in any ways patronising or sarcastic...
Go walking, do ridges. Don't get a heavy pack on purpose: on the contrary get into good habits and start making it as light as is safe.
Re strength: go climb winter stuff lots. If that's not available (time, money...) do some dry tooling. At the very worse (which is already a lot) climbing will always be beneficial. If none of the above is available, keep generally fit, and have stamina.
Anyway, winter climbing makes you (for most people anyways) good at winter climbing.
By all means lighten your load when your out but why make your training bag as light as possible? If you're doing one or two up hill load carries a week and you reduce the load you reduce the training. Training needs to be hard, if you keep trying to make it easier your only wasting your own time.
If you can do a few runs a week, strengthen your quads and calfs and do 1 load carry a week you shouldn't have any trouble with fitness. For your load carries just fill your bag with 15-30 kg of weight and walk uphill, if you make as much of that weight as possible water (bottled obviously) you can pour it out at the summit and jog back down.
Anything which has you gasping for breath is good news.
So checking my bank balance then?
or lack of balance anyhow
http://bobwightman.co.uk/ Good website for fell running information
http://www.brianmac.co.uk/index.htm Good website for sports related science
For good ideas that can be applied for mountain sport read Mark Twights Extreme Alpinism.
Flogging up hills with a heavy sack is what you are training for, so fairly obviously that is what you should ideally do. Over the autumn, put on your heaviest boots and make your sack noticeably heavier than you will be carrying for winter climbing so that it feels rewardingly light when you actually go climbing. If you are worried about your knees descending, carry the extra weight in water and empty it at the top.
Of course running is less time consuming and for many people more convenient, so do that when you can't get to the mountains and include as much uphill as possible.
Once winter starts,save yourself for the real thing! I(assuming you can get out regularly).
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