Anyway to extend suggested workout warmup time?

If you are training for a specific event, you should probably use a training plan aimed at that event. Garmin Coach offer 5K, 10K and half marathon plans that have similar pace targetted workouts.

Depending on the workout warming up is needed more or less.  If you are doing 20-40minutes of Tempo, warming up isn't as important compared to a day of sprints or hard intervals.   Also everyone is a different (as is their warmup intesnity), 20-25minutes is a good long warmup for a lot of people, 20-3 miles or warmup for me before doing a Tempo run?  Not really needed usually feeling pretty warm and fine to go after 7-12minutes.  Everyone is different i guess.  Also some people a 25minute warmup would be almost their entire run (or longer!)! haha  BUT, yes you should be able to have as long as you want.  I thought when I used that feature that the warmup was as long as you wanted and you pressed the lap button to enter the workout portion?  Maybe I'm thinking of the 'Intervals' workout choice... hmm

As far as workout variety, yes it will throw all types at you, I would assume it is basing it off your current training volume, training load focus (ana, hard aero, easy aerobic).  I have seen plenty of shorter sprint work in the past, don't look at it much these days as my training has been indoors in the winter (no vo2max results to set training status)

There is not a way to change the warm up time for the workout; however if you would like to extend the warm up time, you can recreate the workout in connect and send it to the watch. For example todays DSW was a 10 minute warm up at 7:05, 4 x 6 minutes @ 5:50 pace 2 minutes at 8:05 for recovery 10 minutes cool down at 7:05. If I wanted to extend that I can set that workout in Garmin Connect. By nature the DSW is prepopulated and automated so there isn't a way to manually set it. Nick's suggestion as well is another way to set up the workout (intervals on the watch) the only thing with that would be no individual segment alerts. If you don't use/don't like the alerts that would be a quicker way to give you manual control of the workout. 

Brooks - it's odd to me that the DSW has a 10minute... yet with the  Training / 'Intervals' option you can have choices to turn off warmup and also the warmup is until you hit LAP.  Seems like the DSW would at least take that precedent and use 'warmup until Lap Press' ?  Granted for many people 5-10minutes of easy running with a few pickups thrown in is typically fine.  Just seems like the 'lap button press' option is typically the best for warmups (whenever I setup a workout custom I do that or longer than needed for me (15-20min), knowing that i'll likely hit lap key.)

The best terrain for my work out is 15 mins from my house. I just push the stop button right before 10 mins and then hit it again when I’m at my work out terrain.
I  know I will miss about 5 mins of warm up run but don’t really care.  On the way home, I just have an additional 5mins of cool down.  

I have the same problem! I live in a dense city, and usually I need a few more minutes to get to the place where I can do my sprints.

Have you added a feature suggestion for this?

Just an idea, but you can pause the activity and keep on doing the warm-up, then start again when ready. Or start your light jog, start the activity 5-10 minutes in.

Same for me. Starting an interval right in before a hill is not something I wanna do. Would just need 5 more minutes to get to a flat spot. Warmup untill lap pressed or a convenient way to copy and modify a DSW would be very appreciated.