This is a very well written description of the statue from Discovery Thailand:
Being so centrally located, the equestrian statue of King Chulalongkorn (Rama V) is well worth a visit. A forward thinking monarch, King Chulalongkorn is revered as the man who elevated Thailand’s status in the world by abolishing slavery and forming strong allegiances with the world’s then ‘superpowers’ - Britain, France, America and Russia. During his 42-year reign he travelled widely, forging strong ties with neighbouring countries and the royalty of Europe. Modern Thailand would probably look very different without his efforts on the world stage. However, the historical significance of this great man is only part of the reason for a visit to his statue. Another reason is his followers.
Over the years, many Thai’s respect for their former monarch has grown to a point where he is now the object of worship. There is a firm belief in the former king’s ability to bring good fortune, especially to those in business. Devotees place candles and incense sticks at the foot of the statue and leave gifts of flowers and brandy – the monarch’s favourite drink – in the hope their prayers will be answered. Tuesday (the day Chulalongkorn was born) sees most activity with countless people lost in prayer around the statue.
I visited the statue on 24th October 2006, which was a day after "Chulalongkorn Day". Thus, it explains why in the photos, there were so many offerings surrounding the statue.
If you're in the vicinity of the Marble Temple, it's worth walking the short distance around the corner to see the attractive equestrian statue of King Chulalongkorn (also known as King Rama V).
King Chulalongkorn was a great reforming monarch and was responsible for much of the modernisation that took place in Thailand during his long reign from 1868 to 1910. There's a great webpage about the King on the website of the university that bears his name: