Throat positions and voicings change over the range of any sax, but the embouchure stays largely unchanged (there are subtle differences needed, but does stay largely loose and unchanged).
Is it hard from trumpet to sax? Ornette Coleman didn't think so! He doubled Sax and Trumpet (his primary was Alto Sax).
If you're doing a solid switch, an not a double, you can concentrate just on sax, and pick trumpet up again later, if so desired. It's usually a good idea to have one type of embouchure firmly developed before adding another. If not, than bad habits on both can develop!