In the context of wind turbine pitch control for load alleviation or active wake mixing, it is relevant to provide the time- and space-varying wind conditions as an input to the controller. Apart from classical wind measurement techniques, blade-load-based estimators can also be used to sense the incoming wind. These consider blades to be sensors of the flow and rely on having access to the operating parameters and measuring the blade loads. In this paper, we wish to verify how robust such estimators are to the control strategy active on the turbine, as it impacts both operating parameters and loads. We use an extended Kalman filter (EKF) to estimate the incoming wind conditions based on the blade bending moments. The internal model in the EKF relies on the blade element momentum (BEM) theory in which we propose accounting for delays between pitch action and blade loads by including dynamic effects. Using large-eddy simulations (LESs) to test the estimator, we show that accounting for the dynamic effects in the BEM formulation is needed to maintain the estimator accuracy when dynamic wake mixing control is active.