You can walk or ski pretty much anywhere in the countryside. The exceptions are to ensure that you do not disturb and do not destroy. For example, you must not intrude on the grounds of a house or cross cultivated ground.
People who live close to natural areas have the right to enjoy their homes undisturbed. This is why you must not to walk or ski across the grounds of a house.
‘Grounds’ in this context means the area immediately around a dwelling house. There are no rules laying down a minimum distance – what matters is the risk of causing disturbance.
Cultivated ground mainly refers to gardens, plant nurseries, park plantations and similar sensitive areas. You must not cross the grounds of a house or cultivated ground at any time, whether or not there is a risk of damage to the ground or vegetation.
There may be other grounds which you must not cross if damage might result. A forest plantation of tender tree plants should probably be seen as off limits for the same reason.
Another example that is often mentioned is growing crops. During the time of year when the crop is susceptible to damage you must keep out. But when the ground is frozen and snow-covered, there is no reason why you should not cross a crop field on foot or on skis.
The Right of Public Access is subject to the condition that you do not cause damage or other nuisance. For this reason it would be hard to claim that it applies to a golf course – at any rate not during play and not on the greens (the closely cropped areas around the holes).
The greens in particular are so sensitive that walking on them would probably count as trespassing.
Greens can be damaged by skiing and walking in winter too, and any fences or barriers must be respected. But as long as you keep off the greens and tees (the areas where the players make the first stroke of each hole), you are generally allowed on a golf course while play is not in progress.