For headphones, anything by Etymotic or Shure is a sure thing (hah hah). The Etymotic ER-6i are an incredible value, street price of around $90. They are iPod trendwhore white, but the ER-6 are black. The ER-6 are higher impedence (lower impedence is better for portables) and have slightly less bass response. Also, all the Etymotic phones are a little lean on bass. A good EQ can take care of that but I'm not sure how good the iRivers' are. The Shure E2c and E3c are within your budget I think. Infact, the E3c might be a little over $100, but worth it over th E2c. The general consensus on Head-Fi and my personal opinion is that the ER-6i trump the E2cs, with the exception of bass. Etymotics are known for their insane detail - you can hear stuff you've never heard before on the ER-6/ER-6i. They can bring out flaws in low bitrate MP3s, but I don't find it that big a deal.
And then there's the Sony MDR-EX71, EX81 and probably a few others. They're supposed to be pretty good, but a lot of people say they lack midrange and are all bass and treble. There's also the Sharp MD-33 and a ton of rebranded versions by many companies (there are of the EX buds too). The Shure and Etymotics are real canalphones - they insert into your ear canal and isolate over 20 dBa of ambient noise. The Sonys and the Sharps, not so much. Maybe 10-15 dBa? I forget.
Then there's the Audio-Technica buds, which are supposed to be quite good. Unfortunately they're a little pricey since they're imported.
And if you don't mind clip-ons, nothing beats the Koss KSC-75 for their price. Street price is around $15, but don't let the price fool you - I've got a pair of these and they compete with headphones in the sub $100 range. With a headphone amplifier and impedence adapter, they can outperform $100 headphones. Of course that's no concern to you probably, just making a point. The KSC-35 are the same thing but black, not the 1950's space ship silver of the 75 (it doesn't help that they look like flying saucers, too). The KSC-55 also use the same drivers but in a behind the neck form. There's also the Portapro and Portapro 2, which are over the head sport phones (the Portapro 2 actually converts to behind the neck) and sound very similar to the 35/55/75 since they also use the same drivers. They're just a little different because of the enclosure and how they press against your head. They're also a little expensive and quite ugly.
So there you have it...all the best options for portables I can think of. Personally, I would go with the ER-6i by Etymotic. I have the ER-6 and the value is just incredible.
Oh, and FG, about the cold...players shouldn't be affected. Hard drives MIGHT because of the moving parts, but you'd need extreme cold (yeah, you're in Finland, I know) to freeze the moving parts and counteract the heat generated by said parts. Also, LCDs get ghosty and slow in the cold, like they have a high response time. They can also get dimmer I believe.
Bassoon, n. A brazen instrument into which a fool blows out his brains.