Basically the inclement weather policy is normally just about what happens if it snows. Presuming you're not from the UK originally a short explanation :
Basically every few years, we get a 'reasonable' amount of snow, that's reasonable for the UK ie we get maybe 3-5cm (am talking about in Cambridge area) over a few hours. Unlike where you're from we don't have the infrastructure or kit to really handle that amount of snow so it causes a disproportionate amount of disruption sometimes, especially if it falls overnight when no-one is on the roads or very fast during the working day and buggers up rush hour.
Schools will have a policy that states generally they will try to keep the school open, explain how to find out if it's closed (generally check the website but also local radio may announce it) but with the caveat that it's down to parents to decide if the journey in is safe or not. Similarly if it snows hard during the day and you live out in the sticks you have the right to get your kids before it gets bad.
To give you an idea, we've had bugger all snow for the last few years. About 9 or 10 years ago we randomly had about 3 winters on the trot when it snowed quite hard in the run up to Christmas. About 15 years ago, the snow came in from the North East suddenly during the afternoon, Cambridge was totally gridlocked and the M11 (main motorway that goes to the west of Cambridge was blocked and 100s of people spent the night in their cars). It took me 5 hours to cross from one side of Cambridge to the other and I gave up trying to get home at Duxford (village outside Cambridge) and spent the night at friends, the following day all the schools were shut.
Cambridge has an odd microclimate - the biggest problem is the wind which if it's coming from the East is bitterly cold (there are no mountains/hills between us and Scandinavia/North Eastern Europe/Russia). I used to live in South Germany where it got to -14 at night and not above freezing in January at all but could find Cambridge bitingly cold on those windy days. They are not constant though, it will be random days.
Depending on the age of your kids you might find that even though they have all the cold weather gear, they might not wear it - it's a British thing, wearing coats as a teenager is not cool. I never wore one although I sure as hell do now.
Basically hats, scarves, coats and gloves will do you. Again we don't have the need for (or culture) of furry/fleece lined boots, lots of layers etc. It will definitely feel warmer than where you're from though.
March/April could go either way - we've had snow and frost at Easter occasionally if it's early in the spring, equally it can be in the teens and lovely and mild - at which point everyone will crack out the Summer clothes in case we don't get a decent summer. We like to make the most of any weather that isn't grey and drizzly - hence we will make snowmen when there's barely a covering and BBQ when the temperature hits about 17 degrees .