This is a question which you'd think I'd know the answer to, beyond "A big pointy thing with snow on top". But, for the sake of what gets included here and in the magazine, it's important to have a clear definition.
Using a variety of sources, and bearing in mind that this isn't "Hills Magazine", I've come up with the following to let you know what, geologically, I consider a mountain:
Perhaps the most important definition of all. At what height can something be considered a mountain? Britannica states that the term "has no standardized geological meaning". According to a variety of sources, including Ordnance Survey (which has this wonderful guide to the large number of names we call hills and mountains in the UK) it's 610 metres, or 2,000ft.
A mountain could be thousands of metres high but just a couple of metres above the surrounding terrain. Prominence is therefore also an important factor. The Merriam-Webster definition is "a landmass that projects conspicuously above its surroundings". National Geographic states that many geographers put a number of 300 metres' prominence over the surrounding area (land or sea).
This is a much easier one to answer. Because mountains are found in comparatively hot climates it's possible that they can easily meet the height criteria yet never get snowed on. Although there are mountains in the tropics which have snow (Kilimanjaro being just one example) many do not, yet that doesn't make them any less mountainous.
Does a mountain need to be pointy? Not necessarily, but there must also be a limit to the size of its peak area otherwise it would be a plateau. But what is that size? Again, there's no definition. There are many flat-topped mountains, with Grand Mesa, Table Mountain and Mount Roraima being just some with particularly large summit areas. The latter has the largest summit area and so that will be our maximum
In conclusion: it's hard to make a definitive conclusion. According to Wikipedia the UN Environmental Programme's definition of "mountainous environment" has seven different classifications, with Class 1 having an elevation greater than 4,500 m. The International Climbing and Mountaineering Federation has different mountain classes for the Alps, Pyrenees, and Himalayan and Karakoram regions. However, because this is a UK-based publication, our answers are clear. A mountain is therefore: