While short hamstrings could be causing your "butt wink", other things could be causing you to lose your arch as you approach the bottom of the squat as well. So, you might want to check into the possible tight and overactive hamstrings a bit more, IMHO. In fact, tight hip flexors is usually more common but that is because more and more people are sitting at desk jobs than ever before. This may or may not apply to you. If you do have a desk job or spend a great deal of time sitting, then the odds of you having inhibited hip flexors is diminished. They are engaged a majority of the time.
I would try doing two quick tests. First do a standing Psoas test. The psoas is the only hip flexor that is active over 90 degrees so it is easy to isolate and test. Stand up, pull your knee to your chest (you can use your arms). Once your knee is to your chest (or close. Must be well above 90 degrees though), let go. If you are able to keep your knee up above 90 degrees for at least 10-15 seconds, your psoas is not weak and this means that it is far less likely that it and the other hip flexors are being dominated. [Edit to add:] Do this test either standing against the wall or at least in front of a mirror. Your back should be straight. If you are keeping your leg up by bending back, then you fail the test. You must be keeping the knee above 90 degrees by using your psoas only.
Next, I would get a foam roll (they are cheap but a valuable tool) and roll your hamstrings. If they are tight and overactive, foam rolling them will be quite uncomfortable and you will be actually able to feel the "knots" as you roll. Of course, if you've never foam rolled, you will automatically be quite uncomfortable, but compare it to other areas such as your calfs and quads. If you feel much more discomfort in the hamstrings, it is likely tight and not returned to resting length. If it is more comfortable than rolling the other areas, then it is not as likely to be shortened.
If all evidence points to shortened hamstrings (and that definitely is not established yet), stretching will help lengthening it. I would also foam roll this area regularly to "untie those knots" so that it can be lengthened and stretched affectively. The foam roll is basically a cheap self massage tool. Of course, this does not solve the reason why it is shortened in the first place and even after stretching and lengthening the muscle, it will return to a shortened state if you don't get those hip flexors doing their fair share of the work.
Make sure you activate the hip flexors prior to your workouts as part of a dynamic workout by doing. You can take 20 steps while alternatingly pulling your knees to your chest. This will turn the hip flexors on so when you work out, they will be easier to engage.
I would also do step ups with a shorter stride and putting more weight on the middle of the foot instead of the heel, this will make the exercise a bit more quad dominant (the rectus femoris is a hip flexor) and will use the hamstring less, I would also add a knee raise at the top of the movement to again emphasize the psoas.
Also, any movements that you are doing that work primarily the hamstring, I would suspend until the imbalance is rectified.
If the psoas test and foam roll do not point towards tight and overactive hamstrings (and this doesn't conclusively rule them out), the problem could be elsewhere (poor flexibility, poor ankle mobility, weak glutes, poor form, etc). Continue to look for the problem. You need more evidence at this point IMHO. The stretching, foam rolling, and adding the dynamic mobility drills won't hurt in any case. However, before I cut out the hamstring work and focus more on the hip flexors, I would would want to make sure that the hamstrings are the issue as we don't want to create an imbalance by attempting to correct one that doesn't exist.
In any case, only squat as far as you can while maintaining your arch. Once you lose your arch, do not descend any further even if it that means you are not yet squatting to parallel. Keep good form first, then try to increase range of motion. Don't go for range of motion if it means breaking form.
This video also works on the issue of losing the arch at the bottom of the squat.
In fact, if you will probably find the whole SquatRX series helpful.
As for the hip extensions. If your problem is overactive hamstrings, then working the hamstrings more (they are a hip extensor and knee flexor) would be contraindicated.