Ice Climbers is an un-tradable item. The only ways to obtain this item is to either pay for an Action Replay for your GameCube (not recommended) or to get the actual e-Card, e-Reader, and GameBoy Advance/Gameboy Advance SP, and a Gamecube to GameBoy Advance Link Cable
I cannot explain the Action Replay, but I can explain e-Cards.
An e-Card is an actual item in real life, a long time ago when the game was first released in America, they (Nintendo) sold packets of cards, (e-Cards) And they also sold e-Readers. Each e-Card had a 'dot code' on the back of it, when you used the e-Reader with the GameBoy Advance/GameBoy Advance SP you would scan the dot code, sometimes this would unlock the a game to play on the GameBoy or sometimes you could connect the Gameboy e-Reader with your GameCube to Gameboy Advance Link Cable and you could get exclusive items (i.e. Ice Climbers NES). Although without a GameCube to Gameboy Advance Link Cable on Animal Crossing e-Cards you could still get some items, they had mini-games on the e-Cards and if you scanned Animal Crossing Character cards (e-Cards with Characters) and picked a certain one and 'won' the mini-game it would give you a code. You would then give the code to Tom Nook who would give you the item. Although if you only had the e-Cards most of the Character Cards had these codes too.
Their were a total of
5 different types of Animal Crossing e-Cards:
Character Cards - Had the Characters picture on it, with dot codes for e-Reader, plus a code for the game if you didn't own a Gamecube to Gameboy Advance Link Cable/Gameboy Advance/e-Reader.
Design Cards - Had a design on them. If you had a Gamecube to Gameboy Advance Link Cable with a Gameboy Advance and an e-Reader you could scan the dot code on the back and it would give you the design on the card. If you didn't have a Gamecube to Gameboy Advance Link Cable/Gameboy Advance/e-Reader you could simply the design on the card (tedious, I know).
Town Tune Cards - Had a Town Tune on them (most were just songs from K. K. Slider). They contained a dot code on them, when scanned would give you that Town Tune. If you didn't have a Gamecube to Gameboy Advance Link Cable/Gameboy Advance/e-Reader you could simply copy the Town Tune that was printed on the back of the e-Card.
Player Cards - Contained a players picture on the front with 2 dot codes on the back, when scanned with an e-Reader you could play a mini-game, then scan a
Character Card and if you choose the correct one you would be given a code, you then can give this code to Tom Nook, who would then give you the item. If you didn't have a Gamecube to Gameboy Advance Link Cable/Gameboy Advance/e-Reader these cards could not be used.
NES Cards (Rare) - These cards required a Gamecube to Gameboy Advance Link Cable, GameBoy Advance and e-Reader, you would scan the dot code on the back and when you scan it Tom Nook would send you a letter containing the NES. This NES could
not be obtained anywhere else in the game (excluding hacking). These NES's also cannot be obtained using Universal Codes as none of them exist for these.
You can buy these cards from e-Bay if someone is selling them.
The Online Nintendo Store is
currently selling one pack which is the
Animal Crossing-e Card Pack - Series 4 Since these cards are no longer in production, they only have a limited amount of these, They are pretty cheap to ($3.29 U.S./ about 2.45€ [euros]) So get them while they still have them!