It is very doubtful that the typical PVC outer sheath cable cover will resist UV, heat or freeze/thaw for very long before it starts to harden and crack, exposing the inner wiring to moisture. Plus, by taking such a round-about routing you are adding a lot of extra length to the cable with the possibility of signal loss.
If you have to run the HDMI cable outside, put it in conduit, not stuffed under vinyl siding