L@ser based speed sensors are in R&D phase
LDA, L@ser Doppler Anenometry, is used in wind tunnels for at least 25 years now. It works perfectly.
The only issue: now you do not have only one hole to clog, but (simply stating) two l@ser and one camera to be covered by ice... So the risk of failure is trippled.
You may operate it through the cockpit window just like some optical devices on modern cars, so icing/contamination of the windscreen is evident to the pilot and can be counteracted by the wipeers or the window anti-ice. But pitot heat off should be evident to the pilot as well....