In reply to girlymonkey: I've had to arrest three times (once with a technical tool) for real over 27 years. I've probably had to self belay a dozen times.
I still like to use an old fashioned model for how I think about keeping myself safe walking on snow and teaching it to others:
STEP. Walking isn't too technical a skill to learn and the good news is that I can practise it every time I'm out. Perfect practise makes for perfect performance so by focusing on always walking well my technique gets better and I'm less likely to slip.
SLIP. If I do slip then immediately stopping myself by driving my weight down onto my axe so that the shaft is driven in (that's why its important to carry the axe vertically and not to far away from my side) / if using a more technical tool or with very hard snow I'll be looking to get my pick in in the basic self arrest position. This also requires a relatively low skill and can be practised quite easily at little cost of time (subject to picking a good venue etc.). If I blow this then I'm sliding.
SLIDE. Self arrest for me is an essential but complex skill. For even the basic position there is a lot to remember. Heels up, hips up, knees wide, look down the shaft, cover the spike, adze into the right place on the shoulder, don't drive the pick in to fast or you might lose it in firm snow. Then you have to get there first. Even on a clean fall are you feet first facing in? Feet first facing out? Head first in? Head first out? And all that assumes that a heavy rucksack isn't holding you on your side or you aren't tumbling out of control. On 'easy' snow you will get away with a scruffy arrest. On harder stuff if you don't get everything right and get your weight over an axe whilst gradually applying pressure you are unlikely to stop. On a steep slope of the bone hard stuff around recently- good luck, you will need it. And you need to look at what to do if you drop our axe/lose control of it at the end of a leash.
STOP. This is what its all about. Prevention is better than cure but the reality of an unexpected slide on hard snow means its going to be very difficult/impossible if you get any momentum up.
So if I'm teaching i think of it as a pyramid. At the base of it I put most emphasis on the skill we are able to practise most and get really good at- walking well as much as possible, staying aware of terrain underfoot and choosing a good line. The next tier I put lots of emphasis on as we can practise it a lot easily and its not too complex- self belay to prevent a slide. At the top of the tiers is the hardest skill to master well and the one that we probably get least practise at- self arrest.
N.B. I'd never ignore self arrest when trying to help people become independent winter hillgoers. Its a vital skill to be aware of and its saved my bacon 3 times. But in terms of emphasis I prefer to spend more time ensuring we are walking well, choosing a good route and staying aware of the 'what ifs'. "What if I slipped here? How would I stop myself (self belay)". I go out early in the season and practise every year but am reluctant to rely on a complex skill I get limited practise with even though I spend time teaching it every winter. Its about emphasis not either/or.
I always teach step cutting too. Even with crampons on a few steps can allow a rest or increase security on a slope (as well being useful for crossing short snow sections without crampons/helping someone with a broken/dropped crampon).
Just my humble opinion.
Technical tools are another matter. I try to make a decision about whether I'm on walking ground (standing upright and using 1 axe as a walking stick, it has to have a spike for me- other one under a shoulder strap) in which case my self belay may well be getting straight into self arrest position before sliding at all OR I'm in climbing mode in which case I've often got 2 tools in hand and I'm daggering and security is reliant on climbing movement and having 1 or both tools in.