Last spring I visited Rùm and I was impressed to get an impression what Scotland might have looked like in the past. The absence of sheep combined with an attempt to reforest part of it gave a dramatically different expression from the deforestation and overgrazing of mainland Scotland, even though the natural ecology is still quite far from beig restored even on Rùm. Are there any other parts of Scotland without sheep and where natural vegetation is given a chance to recover?
It is not just sheep - in many parts of Scotland, the main problem is overgrazing by deer. Especially in the highlands - much of the land is owned by shooting estates, who want to maintain high numbers of deer. These deer can roam over large areas - including the hill tops - eating any young trees that might be growing.
Other issues are trees being felled for timber, and plantations of non-native species.
To see some more natural forest, probably best to look for specific restoration projects. You could look at the conservation charity, Trees for Life, their aim is to restore the Caledonian Forest across the highlands. Much of their work involves fencing off areas to control deer numbers, and planting native trees within, as well as removing non-native species.
Most of this project is focussed on an area to the west of Loch Ness, around Glen Affric, Glen Moriston, and Glen Garry. Probably the best example is Glen Affric - it has plenty of old Scots pine, but few young trees were managing to grow, due to the deer. Several areas have been fenced off over the last 20 years, so you can see what a difference this is making. As well as young trees, there is a variety of other plants and wildlife growing much better. Glen Affric has plenty of impressive scenery, including lochs, mountains, and forests, so is certainly worth visiting anyway. Trees for Life have a map and more details of specific sites where they have been planting.
Rùm is an interesting example. It has had a variety of owners over the centuries, who have impacted on the island in a variety of ways. Yes, it doesn't have any sheep now, but still has a lot of deer, and a few goats roaming the hills. Now that it is a national nature reserve, there is some work going on to research the deer, and control the numbers. As well as several areas being fenced, and planted with native trees. But much of the island is not exactly 'natural', even though it may seem quite wild.