Important considerations when learning ice axe arrest are perhaps not the earliest for a 'beginner' to discern. Such as snow condition, run-out risk and the consequences of someone losing their axe (don't train with a leash, for example). Whilst many people can and do practice - they typically have some kind of knowledge or experience first so they can make those decisions better.
Overall though Snowdon via the Llanberis or Ranger paths are not a significant undertaking in the summer - but you need to have respect for the conditions in the winter - be aware of the freezing level and whether there are reports of ice or snow at higher elevations. The last thing you want as an inexperienced party is to be slipping around trying to get to the top, especially when there are typically more accidents when descending.
Minimum equipment would be microspikes and trekking poles/axe as well as proper footwear, but I'd be concerned someone in the group is at least a competent navigator - as has been said, often you'll be walking through low cloud in winter and having a disoriented group start to drift away off-route can turn a quick up and down into several hours of wandering. This is especially likely in winter when mild hypothermia can rob the mind of the ability to logically think through navigation - you'll often see experienced winter walkers writing bearings and directions on their maps to stop them having to think about it if poor conditions are expected.
Lastly, don't feel put-off - renting kit is cheap, often some more experienced people have spares they can lend you too. Overall I see it a little like owning car insurance - sure you don't need it to physically drive a car, but there will be a number of times where you are really glad you spent that money as it gets you out of a tough spot.