Abstract: To address the safety challenges of connected operations for risers and subsea wellhead under low-speed level ice or slow ice-crushing conditions, a quasi-static coupled mechanical model of the floating drilling platform-tensioner-riser-subsea wellhead system was established by comprehensively considering ice force, current force, tension force, soil resistance, and the large lateral displacement effect of the riser. A one-dimensional bidirectional search method was proposed to determine the critical values of the operation envelope. The results showed that the connected drilling operation envelope was mainly constrained by rotation angles of flex joints and presented an inverted cone shape, shifting downstream of the well location under ice loads. An increase in ice thickness significantly narrowed the drilling operation envelope, whereas increasing the initial top tension and reducing the drilling fluid density helped broaden the operation envelope. The bending moment of subsea wellhead and the rotation angle of the upper flex joint were the dominant limiting factors for the connected non-drilling and emergency disconnect operation envelopes. The research findings can provide theoretical support for the design of quasi-static connected operation parameters and operation risk management in polar ice regions.