If you wax an article that hasn't been waxed before you're going to need a lot of wax and a lot of time; it'll disappear at a frightening rate, it has to go right into the fibres to be effective and you'll need to "drive" it in with a brush or cloth and the help of a heat gun or hair dryer; it's not hard to do but requires a good deal of time and effort.
What you end up with will be heavy with the weight of the wax, much darker in colour, totally waterproof and completely unable to breathe at all - like Barbour and all the other makes, not the best things to be walking or working in, far too hot for most. I've done it a few times many years ago and the results were just unwearable except in the very coldest of weather, and then they're not the ideal thing for those conditions.
The other thing to consider; you'd be better to make a mix of two parts beeswax to one part each of pure turpentine and boiled linseed oil. Warm them all together and mix thoroughly, leave to cool and then apply.
If you use wax alone it'll be very hard, will crack where you move, i.e. elbows pockets etc., whereas the above mixture will sit in the fibres rather than on them.
I'd think very hard before I did this to a cadet smock, you'd ruin it, in my view, and there's no going back! You might be better off trading your smock for a wax jacket? I've wanted one of those smocks for years and up 'till now haven't found one.............................One day, I hope!
Be very careful if you make up the above mixture - it's extremely flammable when molten so it's best to do it in a double pot with hot water, bain-marie style.