Apart from TinMan and tthew everything else said above is complete tosh. Yes you can try to claim from the local council, but not under H&S law as highways are expressly excluded from the definition of a 'workplace'.
The Government changed the law in 2003 to place a legal duty on highway authorities to try to keep highways clear of snow and ice and they have to take reasonable steps to do so.
As a defendant lawyer I would argue on behalf of the authority that in these exceptional conditions they are doing all they reasonably can in prioritising the main roads. Your lawyer would argue that by now they should have worked their way down the list to the more minor roads and pavements. The fact that the Government has now instructed highway authorities to cut gritting by 25% adds an interesting complication.
The warning to people not to travel carries no legal weight but again I would argue that you should have stayed indoors/worn better footwear/taken more care.
Any claims in current circumstances are likely to be difficult but no doubt there will be some as there have already been some very serious injuries.
In an employment situation your employer has a duty to risk assess and to take appropriate steps to reduce the risk, including to provide suitable PPE.