There have been particular efforts to keep open schools for exams
Schools where pupils are taking GCSEs and A-levels have been given priority treatment in clearing away snow to help exams to go ahead as planned.
England's exams watchdog, Ofqual, says early indications suggest this has been a success, with exam centres kept open.
But in Hampshire, there were reports of pupils unable to reach their exams.
Pupils in England, Wales and Northern Ireland have exams scheduled for this week - and there have been worries that the bad weather could cause problems.
Ofqual says that it has held meetings with exam boards on Monday to monitor the impact of the weather.
"The early indications are that most centres have been able to proceed with the exams or make alternative arrangements for their candidates," says the exam watchdog's statement.
But in Alton College in east Hampshire, 40 pupils out of 320 failed to arrive on time for their A-level papers - with a number of these arriving late.
"It hasn't been satisfactory, but we're doing what we can," said principal Jane Machell.
"We have had lots of parents trying to bring them in, others have been staying overnight with friends who live nearby," she said.
But overall it seems as though most schools have been able to remain open for pupils taking exams - with some snowbound schools only opening for these exam candidates.
Across the UK, about 850 schools were partially or fully closed on Monday because of bad weather.
In Northamptonshire, the council says that it made particular efforts to clear a path to 18 exam centres.
A spokeswoman said that this had been successful and that "everyone who should be taking exams will be".
Isabel Nisbet, acting chief executive of Ofqual, said that it had been the right decision to press on with holding exams this week.
"The best thing is for young people to do the exams when they planned to do it, because they've been working all over the holidays for them and you can see that's part of their learning plan," said told BBC Breakfast.
"The best thing is for them to do it, and the fairest thing for everybody is for as many as possible who can do it, to do it.
"We have looked at all the other possible things that could be done, in fact there's a whole programme of exams that go on right until the first week in February so they don't clash with each other, so postponing is not an easy thing."
Pupils who do not manage to get to an exam centre might have to take them in the summer instead - and there are also contingencies for "special considerations" in which pupils can be graded on other work.
This might more usually apply in cases where pupils are ill or face particular problems, such as bereavement.
There have also been recent cases of large numbers of pupils being unable to take exams, such as the floods around Hull two years ago.
There are still about 160 schools closed in Wales, but many of the schools closed in England last week have now re-opened. Problems still remain in West Yorkshire where 94 schools are shut and in Kent, where 108 have remained closed.
Children's Secretary Ed Balls says that "schools should open if at all possible".
"Heads have got difficult judgments to make. I am sure no head wants to close their school if they can avoid it. But it is really important to take a balanced view and not to overstate risks like slipping in the playground, or having slightly less supervision."