Abstract: Under low-speed level ice or slow ice crushing conditions in polar ice regions, ice loads can induce complicated mechanical responses of the riser-subsea wellhead system and threaten the safety of connected operations. A quasi-static coupled mechanical model of the floating drilling platform-tensioner-riser-subsea wellhead system is established, which comprehensively incorporates ice force, current force, nonlinear tensioner force, soil resistance and large lateral displacement of the riser. A one-dimensional bidirectional search method is proposed to determine the critical platform offset of the operation envelope. The results show that the connected drilling envelope is governed by the rotation angles of flex joints and presents an inverted-cone shape, which shifts downstream of the well location under ice loading. Increasing ice thickness significantly narrows the safe drilling envelope, while properly raising the initial top tension and reducing drilling fluid density can expand the operation boundary. The bending moment of subsea wellhead and rotation angle of upper flex joint are the dominant limiting factors for the connected non-drilling and emergency disconnect envelopes. The findings can provide theoretical support for parameter optimization and structural risk prevention of quasi-static connected operations in polar ice regions.