Officially, Disney has not announced an opening date for their parks. So far all they’ve said is “until further notice”. However, when you try to book a resort reservation at either Disneyland or Disney World, you can only do so after June 1st.
Disney also recently announced a free dining plan for guests impacted by the Corona Closures (conditions apply, call Disney for more information). This plan is good for guests who originally had plans booked March 16 through May 31st. Suggesting that anyone with April or May plans might be forced to reschedule.
Nothing however is official yet & Disney did state at the end of the announcement that it’s still possible the parks open sooner. Please call Disney or your travel agent before making any final decisions about your Disney trip plans.