For the Spartans, physical training was an integral part of their culture. It became necessary, and was required by the government, that they achieve and maintain very high levels of physical fitness and strength endurance.
The Spartans used whatever was available to improve their physical conditioning. Body weight exercises such as push-ups and pull-ups would have been heavily utilized. They would use resistance in their strength training methods by using stones, rocks, logs, animals and each other to help increase their strength. Wrestling, running, jumping and climbing were all part of their training regime.
All of this training was done outdoors and exposed to the elements.
Training for a Spartan meant improvisation and adaption. It focused on what they were capable of enduring while maintaining a high level of efficiency throughout. Not unlike the modern day special operator.