In reply to Nao:
Just back from a trip 4 wk trip to Chile over xmas & NY which included TDP and El Chalten as well as lakes and then north to the Atacama.
We treked the "W" in the TDP over 4 days/3 nights and then travelled to El Chalten via El Calafate. Spent 4 days/3 nights in El Chalten/Glacieres park. Both wonderful places.
We didn't use guides and the treking was reasonably straighforward and guidance trek times OK (we camped). Refugios avail in TDP or you can camp and eat in refugios also - book in advance though (and check that your timing isn't too early for them). All fixed tents for hire if you want to save your back.
-ve side is that the routes in the national parks are busy-ish (we went in late Dec which I'm sure contributed to this) with an array of folks clutching their lonely planet - despite the remote feel getting there.
Got the impression that if you want to do more serious stuff you need permits and possibly guides. Would be more time-consuming, risk on the weather, but potentially amazing.
We did flight to Santiago and thence to Puerto Arenas with LAN Chile. Note that the PA flight stops off at Puerto Montt in the lakes so it might be possible to have some time there too at a squeeze. Friend of mine went via Beuenes Aires (only SA city you get to from Heathrow)
Unlikely to need your swimsuit at this time of year though!
Please post more info if you want specifics.
Steve