The transfer between Buenos Aires EZE (international) airport and Jorge Newbery/AEP (domestic) airport is like most intra-city airport transfers.
Generally close, the drive can take between 30 minutes and 2+ hours depending on traffic and your driver.
Getting into Buenos Aires Ezeiza, you can prebook a car service, take a bus or take a taxi.
Tienda Leon is a well known transport service worth looking into.
“Aeroparque” is AEP/Jorge Newbery.
The transfer should cost between $15 USD and $40 USD depending on the quality of your transport operation.
In order to get to Chapelco Ski Resort, you have to take a flight to Chapelco local airport.
Chapelco is near to the city of San Martín de los Andes. The airport code is CPC when booking flights to Chapelco.
Only Aerolineas Argentinas flies there, from Buenos Aires / Aeroparque Jorge Newbery (AEP) and Esquel / Esquel Airport (EQS).
Note that if you’re getting to Chapelco internationally, you’ll have to switch airports in Buenos Aires from Ezeiza to Jorge Newbery/AEP airport.
See details here: Airport transfer in Buenos Aires.
The flight between Buenos Aires and Chapelco takes approximately 2 hours.
Of course, being south of the Equator, ski season in Argentina is the opposite of ski season in North America. Generally, ski season in Argentina is as follows.
High season: The high ski season in Argentina is from mid-July to the end of July
Middle season: The middle ski season in Argentina is from the beginning of July to mid-July and the end of July to the end of August
Low season: The low ski season in Argentina is from mid-June to early July and from the end of August to early October
Most ski resorts in Argentina open in mid-June and close by the middle of October.