Digital twins for wide-areas (e.g., smart cities) would fulfill the 6G expectation of merging the physical and digital worlds, abbreviated as "DT-WA". It would incorporate an artificial intelligent (AI) model to simulate and predict the physical world, which needs a constant parameter updating process to keep its fidelity. However, the updating process can consume significant energy, where little work exits. This paper proposes an energy-efficient edge cooperation and data collection scheme. The AI model is partitioned into a large amount of sub-models onto different edge servers (ESs) co-located with access points to simulate every part of the wide-area, which are distributed updated using locally-collected data. To reduce system energy, ESs can choose to become either updating helpers or recipients of their neighboring ESs, based on their available sensors and basic updating convergences. Helpers share their updated parameters with their neighboring recipients to reduce the latter workload. To minimize system energy, the paper further proposes a distributed algorithm to adaptively optimize ESs cooperative identities, data collections and heterogenous resource allocations in the dynamic environment. It incorporates several constraint-release methods and a large-scale multi-agent deep reinforcement learning algorithm. Simulation results show that the proposed scheme can reduce the updating energy in DT-WA compared with baselines.