Firstly yes wheels will make a big difference, fist upgrade you should do. You want something light, less weight at the rim is the most important as it's rotating weight and furthest from the hub. Plenty of folk like Eastons and have a good reputation for durability too. I like Campag wheels and depending on budget work your way up from Zonda to Euros or Neutrons (Neutron better for climbing), of Shamals if you're really flush. If you don't want Campag then Fulcrum Racing 1s would be good, I've had the 3s and they were very good.
Winter bike - yes get one. A dedicated grotty weather bike it better for you (keeps you drier and cleaner and generally happier) and for your good bike. Get one that is a proper winter/tourer, i.e. had braze-ons for full mudguards. Full mudguards mean you can ride whatever the weather and you'll enjoy it more and so will those you ride with. Steel is more comfy than aluminium and probably more long lasting if you look after it and don't let a load of road salt stay on it. A touring frame will have braze-ons for a rack too. You may not want one now but if you use it to commute then it's much better than a bag on your back, or you might just fancy a holiday on it at some point. It would give you flexibility anyway.
If you want a flash ride then you use your good bike so why not make the other one a good workhorse/all-rounder?
Re which frame get one that fits well as that'll be most important. I have a GB steel frame that I picked up last year for £250 with a carbon fork which is great. Very comfy and I can load all kinds of stuff on the rack, it has mudguards on all year, I fitted a dynamo up front for commuting. Basically it does everything for me when I need something other than a race bike. I'm not sure that they still sell them, but if you aren't sold on steel then they sell the Aeron (made by Ridley) aluminium frame which is very good value too. Aluminium winter frames will be more readily available than steel and a lot of steel now will be more specialist and made to order, so quite expensive. It would give you a frame for life from say Bob Jackson or Dave Yates though. Have a google on audax frames and see what you can turn up.
Happy shopping
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Edit:
A quick google for steel audax/winter frames =
[url=http://www.sjscycles.co.uk/category-Thorn-Audax-frames-432.htm]Thorn[/url]
[url=http://www.condorcycles.com/fratello.html]Condor[/url]
[url=http://www.longstaffcycles.com/index.php?main_page=page&id=2&chapter=2]Longstaff[/url]
[url=http://www.daveyatescycles.co.uk/]Dave Yates[/url]
[url=http://www.wilsoncycles.co.uk/frames.htm]Wilson[/url]
[url=http://www.robertscycles.com/products.html]Roberts[/url] in Croydon so you could pop round easily, they are near Cherry Orchard Road.
Made to measure will take longer obviously and I think Dave Yates (who is very popular with the audax set) is renowned for slow delivery.