Having started hill walking back in the pre-internet days, much of first experiences were outwith of winter. I got lost once somewhere around Esk Hause with my pals, and after that unnerving experience vowing it would never happen again, map reading, compass work became second nature (no GPS then). That is to me the most important lesson regardless of the season, and it came easy to me, with my love of maps.
The following years were largely more and more experience across the UK, in different conditions, and this also helps one to focus on that navigation ability and the ned to be able to do it in the worst conditions, it is quite simply fundamental, whether you are continuing your walk or abandoning it
Sometime in the mid 80's I did do a weeks winter skills at Glenmore Lodge, together with much reading of various books, and although it was then on the back burner for many years, it is like riding a bike. However, with the various media available now, it would not be beyond anyone experienced in walking to pick up the basics, and I practised what I had learnt as soon as I began winter walking some years later.
Essentially, the key skills of axe. crampons have been debated here, the axe arrest is something you can practice safely on a suitable slope to ensure that you have the knowledge, it could save your life, it has mine. Crampons are NOT a substitute for axe arrest. Yes they may prevent a slip and are essential on ice, many a summit would not have been reached without them, and when you're only 50 metres away from the top, the last thing you need is to turn back because you simply cannot stand up or make progress.
Lastly, assessing the avalanche risk, I did receive some instruction on this on my winter course, but again some years back, but it too is also something that can be tried whenever you're out in winter. It takes no time to dig a test pit to assess the snow structure, and if used on your planned slope for your walk is the best way to confirm the conditions. Whilst the SAIS information is useful, it may not be specific to the exact area you are going to. This practice has also resulted in my turning back on several occasions, having dug a test pit to establish that the top layer of hard snow was not secure, the test resulting in the top slab giving way. Whilst this demonstrated only a small area, it was clear that ascending further, where the overlying pack would be more frozen higher up, to some point where it would be just perfect to break under my weight. In short, it'll be there another day. The day in question, as I walked out there was avalanche debris (that occurred while I was up the first Munro) on the west slopes. Similar facing slopes that I would have traversed had I continued to the second summit. The first summit was reached that day, as again a test of the snow on the opposite slopes proved secure.
You don't need to be an 'expert' on snow structure, dig a pit, try it, if it shows avalanche potential (and you can read up on what, how that shows), find somewhere else or turn back.
The one thing that repeats in the above, is the knowledge of your ability and knowing when to turn back. I have always been an advocate of going out whatever the forecast, for several reasons, 1: the forecast is often wrong, which can work either way; 2: It is only in the inclement weather that you will hone the skills that should be business as usual, regardless of weather, like navigating (we've all been tired, wet, fed up, and that's when the decisions can go wrong), so stop, think, confirm your position, it is a necessity); 3: You will also find out your limits, what is comfortable, what isn't, everyone is different, its experience