There are three main location categories for analog tests for Mars colonization:
- Lunar base
- Space station
- Biosphere on Earth
A lunar base will have the highest fidelity, providing an environment that is in a vacuum, has no radiation shielding, which is moderately isolated from Earth's resources, and which has reduced gravity. While not an exact analog of Mars, many of the techniques and lessons learned can be applied to Mars colonization.
Currently NASA along with international partners is planning a return trip to the Moon, with a long term goal of establishing a lunar base. However this will take many years just to develop the capabilities of building a lunar base, so in the meantime other analog tests could be considered.
Long terms stays on ISS have already been done, with part of the purpose being to build up experience for long term Mars missions. Longer duration space station stays are possible, ideally on a space station with artificial gravity to simulate the Mars environment. However there are no current plans for such a project, which would also take several years to develop.
You are suggesting a biosphere project on Earth. Besides the Biosphere 2 project that you mentioned, there have been other smaller scale Mars analog tests. A larger scale and duration biosphere type of project could have some benefits in gaining knowledge. However the location is not as important from an analog viewpoint since the facility would be completely enclosed. While prior projects required sunlight, modern lighting technology can now provide a better simulation of Mars lighting and day/night cycles than trying to find a location with similar lighting as Mars. And likely for a fraction of the cost of building, maintaining and supplying a test facility in Antarctica. Also the "resupply missions" to the test facility would likely be timed with the Mars 26 month cycle, which would not necessarily line up with the winter/summer cycles in Antarctica which can limit the schedule for supply missions depending on the location.
However the location does matter in terms of EVA simulations, which would be part of the analog since regular EVA's are expected on Mars. Similar to the ISS analog training that NASA has conducted for many years in the NEEMO project in an underwater laboratory off the coast of Florida. These training simulations include diving activities to simulate doing EVA's.
NEEMO Aquanaut (NASA)
Desert locations have always been preferred for EVA training for the Moon or Mars, and I would expect that this would likely determine the location for a Mars biosphere analog project. Temperature would not really matter since for better fidelity the "bionauts" would likely be wearing temperature controlled suits like they would be on Mars, unlike the coverall and sneaker attire in this lower fidelity Mars analog test:
Mars Desert Research Station (The Mars Society, via Wikimedia Commons, CC-BY-SA-4.0)