To fell a tree to ground level, or leave a stump?

I am about to have a very tall "christmas tree" taken down, as it is way too big for my small front garden.  But I'm wondering whether to leave enough trunk - say 3'-4' - to be able to grow a clematis or other climber over it.  Would that look silly? The trunk is very straight and about 30 cms diameter at the base.  Any thoughts would be much appreciated.

we have recently had a tree felled at my house and a stump was left at wall level i intend to carve out the centre at the front side to sort of 'hollow' it out and then add plants for a feature 

I'd leave it high and as you have suggested grow something over it. Alternatively you could make it more of a feature by turning it into something else, such as a bird table or even a seat. 300mm diameter isn't wide enough to make a seat, but you could add a base such as I did below.

I love tree stumps as a feature in the garden. I love the pics above but even if if you not a carpenter or don't have the tools, you can always do something with them. Even if it's just putting a pot on top of it to raise the height of the garden

Thanks guys - some really interesting suggestions there.

Eddie J, what an ingenious idea and beautiful carving, but a bit beyond me I would have to say!

Thanks happycottontail. That was my first and only attempt at hand carving. I'm more into large scale wood sculpture and chainsaw carving.

The oak tree above is still living and I'm training the new growth up over the seat to form a canopy.

I felt bad cutting the oak tree down, but it had grown very tall and weak. It had been using a 2nd tree for support, which was fine until we needed to remove the major limb on the second tree which had been supporting the oak.

I didn't let the rest of the oak tree go to waste and up turned one branch to form this bird table.

And used the weak section for this.

The holly has now grown up around to frame it.