Definative answer here.. 
From here
http://property.timesonline.co.uk/tol/life_and_style/property/article3205122.ece
"On your own land, it is a different matter. You owe visitors a duty under the Occupiers Liability Act 1984 to take reasonable care to ensure that they are reasonably safe. This means that if you know someone (such as the postman) is likely to walk up your garden path, and you also know that the garden path is slippery, you must take reasonable steps to clear the path of snow and grit it if necessary."
The above is wrong in referring to the 1984 Act. The 1984 Act sets out your duty of care to trespasser, ie burgulars. Yes, you do have a duty of care to burgulars and trespassers entering your land.
The 1957 Act appiles to legitamate visitors, such as postie delivering. Full text below.
1.
Preliminary— (1) The rules enacted by the two next following sections shall have effect, in place of the rules of the common law, to regulate the duty which an occupier of premises owes to his visitors in respect of dangers due to the state of the premises or to things done or omitted to be done on them.
(2) The rules so enacted shall regulate the nature of the duty imposed by law in consequence of a person’s occupation or control of premises and of any invitation or permission he gives (or is to be treated as giving) to another to enter or use the premises, but they shall not alter the rules of the common law as to the persons on whom a duty is so imposed or to whom it is owed; and accordingly for the purpose of the rules so enacted the persons who are to be treated as an occupier and as his visitors are the same (subject to subsection (4) of this section) as the persons who would at common law be treated as an occupier and as his invitees or licensees.
(3) The rules so enacted in relation to an occupier of premises and his visitors shall also apply, in like manner and to the like extent as the principles applicable at common law to an occupier of premises and his invitees or licensees would apply, to regulate—
(a)the obligations of a person occupying or having control over any fixed or moveable structure, including any vessel, vehicle or aircraft; and
(b)the obligations of a person occupying or having control over any premises or structure in respect of damage to property, including the property of persons who are not themselves his visitors.
(4) A person entering any premises in exercise of rights conferred by virtue of an access agreement or order under the National Parks and Access to the M1 Countryside Act 1949, is not, for the purposes of this Act, a visitor of the occupier of those premises.
Annotations:
Marginal Citations
M1 1949 c. 97.
Importand bit now.....Section 2.
2.
Extent of occupier’s ordinary duty— (1) An occupier of premises owes the same duty, the “common duty of care”, to all his visitors, except in so far as he is free to and does extend, restrict, modify or exclude his duty to any visitor or visitors by agreement or otherwise.
(2) The common duty of care is a duty to take such care as in all the circumstances of the case is reasonable to see that the visitor will be reasonably safe in using the premises for the purposes for which he is invited or permitted by the occupier to be there.
(3) The circumstances relevant for the present purpose include the degree of care, and of want of care, which would ordinarily be looked for in such a visitor, so that (for example) in proper cases—
(a)an occupier must be prepared for children to be less careful than adults; and
(b)an occupier may expect that a person, in the exercise of his calling, will appreciate and guard against any special risks ordinarily incident to it, so far as the occupier leaves him free to do so.
(4) In determining whether the occupier of premises has discharged the common duty of care to a visitor, regard is to be had to all the circumstances, so that (for example)—
(a)where damage is caused to a visitor by a danger of which he had been warned by the occupier, the warning is not to be treated without more as absolving the occupier from liability, unless in all the circumstances it was enough to enable the visitor to be reasonably safe; and
(b)where damage is caused to a visitor by a danger due to the faulty execution of any work of construction, maintenance or repair by an independent contractor employed by the occupier, the occupier is not to be treated without more as answerable for the danger if in all the circumstances he had acted reasonably in entrusting the work to an independent contractor and had taken such steps (if any) as he reasonably ought in order to satisfy himself that the contractor was competent and that the work had been properly done.
(5) The common duty of care does not impose on an occupier any obligation to a visitor in respect of risks willingly accepted as his by the visitor (the question whether a risk was so accepted to be decided on the same principles as in other cases in which one person owes a duty of care to another).
(6) For the purposes of this section, persons who enter premises for any purpose in the exercise of a right conferred by law are to be treated as permitted by the occupier to be there for that purpose, whether they in fact have his permission or not.
So, in a nutshell, you must take reasonable care for visitors. The test in law should you be sued would be what would a prudent person due to keep their home safe. That would be, for a fit and capable person, to make and maintain a path. For an old dear, that would be a lower standard of care. Each case is based on it's merits but the suggestion that to do nothing would see you escape liability is nonsense. For a commercial organisation, such as the thread about the supermarket car park, the standard of care is even higher as the supermarket is inviting you on to their premises for commercial gain so they need to look after you.
Hope this helps. Dealing with personal injury claims every day for Insurance companies kind of ingrains this in your head.
But then it snowed again. 
