I just started having this problem a little while after installing 4.3.1 on S3 (no LTE).
Workout app would freeze upon opening and then be responsive 10-20 seconds later, another symptom was my battery life had decreased. I wear the watch overnight (sleep tracking) and it has a 100% charge before bed. In the morning it would be sitting at 94-96% consistently then this problem arises and it started sitting at 80-84%.
I also noticed that when I checked the Usage section in General settings (first thing in morning) of the Watch app on the phone it was saying that watch was active for ~5 hr and standby of ~9 hr. This has been going on for at least a week now.
So today woke up and watch is at 95% charge, usage is 25m, 9 hr standby and Workout app is completely responsive no lag?
The only thing that I can recall doing differently yesterday was installing 3 apps to the watch ( and checking that they worked after install). So I'm wondering if somehow some previous app install was stuck in limbo i.e. trying to install but not quite getting there and thus constantly putting a drain on the CPU and battery and interfering with Workout app being able to start up quickly. Just a theory but perhaps my installing the other apps kickstarted it?