[QUOTE=beowulf;8823456]
he is not what i’d call a daisy cutter, but when i think of ‘daisy cutter’ i don’t think of it as a good mover… around here it seems to be a cutesy way to describe a fairly average trot and canter that IMHO lack impulsion.[/QUOTE]
If that is the definition of daisy cutter in your area, I would wonder about the discipline (AQHA, ApHA, APHA, perhaps?) or knowledge level of the people you are talking too.
In USEF hunters, daisy cutter is the utmost praise. There is nothing average about it.
[QUOTE=beowulf;8823622]
‘toe flicking’ is something else entirely, but many people call that daisy cutting too which IMHO is erroneous as you can have horses with extravagant movement flick and you can have horses with flat movement flick from an old extensor injury; toe flicking is really not a correct way of going.[/QUOTE]
Toe flicking is not daisy cutting. You often see toe flicking in the extended trot of dressage. It’s that extra flip of the foot at the apex of the stride. Some daisy cutters will flick, but not all. To put a visual to the daisy cutter toe flick, it’s like when you show someone your nails. The hand is extended out, but the wrist is not completely extended.
‘daisy cutter’ seems to mean different things to different people; in my local HJ scene a daisy cutter moves like the majority of the horses in this ring (not my video):
https://www.youtube.com/watch?v=5jVDdMvtEwA
but then i see people use ‘daisy cutter’ to describe a horse like this:
https://www.youtube.com/watch?v=G-SY0-ZQNnU
or this:
https://www.youtube.com/watch?v=9YJzsR4ULUQ
i think daisy cutter is a buzz word - meant to generate interest and rarely completely understood.
but – i am an eventer. we need different things. 
It’s true that the term means different things to different people but within the context of USEF Hunters, daisy cutter is pretty understood by the participants and we know one when we see one. For instance, I disagree with vxf111 that a daisy cutter does not have the moment of suspension. Yes, the TBs and even ponies don’t have as much as most WBs, but that doesn’t mean the the movement is no longer daisy cutter.
Not one of the links you posted is an example of daisy cutters. The QH’s are flat movers, but there is no extension, no use of the shoulder. The are all moving very downhill. They would not be successful in a USEF u/s unless there was no company. The other two don’t even approach daisy cutting and I would seriously question anyone that calls them that.
This pony is a daisy cutter The trot at the end of the third video shows it decently. (the beginning of the videos show her not really using herself as well as she can.
doublestable’s big chestnut is a wonderful daisy cutter (although I think she has videos where he is using him self a bit more…taking longer steps with more push than the one when he is young).
The white horse in this video: https://www.youtube.com/watch?v=mMweAoTU-IM
This pony has an amazing canter…but they don’t show the trot at all. https://www.youtube.com/watch?v=E3uLmmYhFns
As you pointed out, you often see a less then perfect jump from the extreme flat movement…it’s why you can’t concentrate on just the trot. The more important gaits are the canter and walk. Usually a good canter means a good jump. There has to be freedom in the shoulder for the jump to be good.
You cannot rely on someone telling you their horse is a “good mover” partly because that definition changes between disciplines, but also because it’s a marketing tactic. Every horse that ever won a hack somewhere is a hack winner.
That doesn’t mean they are a top company hack winner.