The setting for Agatha Christie’s murder mystery play The Mousetrap is the Great Hall of a house in the UK called Monkswell Manor, which has been converted to a guest house. Many of the props and effects are accordingly things you would find and hear in a house. Furniture, a clock, a fireplace, ash trays, and cigarettes help create the post-war setting. In act 1, for example, there’s a pipe belonging to the character Major Metcalf, as well as a radio and a telephone. The radio in particular is of importance to the plot, as one of the characters, Mrs Boyle, is listening to it just before she is murdered. Another important sound effect is the tune "Three Blind Mice," which occurs as part of the plot when Mr. Boyle hears somebody whistling—it was also the original name of the play.
Weather plays an important role in the plot, so unsurprisingly, as the question notes, weather effects like wind and snow are used. One of the characters, Trotter, arrives on a pair of skis.
The gun is a surprising prop, used near the end of the play, during Trotter’s suggested plan to reveal who the murderer is. Another special effect is the sound effect used for the murder of Maureen Lyon at the beginning of the play.
In general, props and special effects are fairly simple and in keeping with the setting of the play: a guest house during an unexpected snowstorm with a group of visitors.