I personally think that an outdoor solemnization ceremony is the most beautiful (worrying about the possibility of rain and combating the heat not withstanding).
Because of the two reasons mentioned, outdoor weddings/solemnizations are not very popular but with these venues you might just change your mind.
I've already mentioned this before but it's worth repeating. The Lawn at Raffles Hotel is elegant, sophisticated. Oh so lovely (and posh too). The downside, it's the lawn so not the best place to be wearing high heels.
Although technically not an outdoor venue, the Art Museum (formerly St Joseph's Institution) has a lovely glassed in venue (The Glass Hall) that has an outdoor-ish feel even though you enjoy the comforts of conditioned air. They also have another beautiful beautiful venue for weddings - The Auditorium. But that's not on the list because it is not an outdoor venue or even close to it.
I think when people say "park" or "garden" in Singapore, the only thing that comes to mind is Singapore Botanical Gardens. And they have a pretty wedding venue to boot.
On top of being a favourite for pre-wedding photography, Fort Canning Park is also a lovely wedding solemnization venue. There are plenty of "venues" within the park that you can choose from. Of course, you can also "cheat" and go for The Legends at Fort Canning.
I found this when I was trying to look for photos of the Orchid Garden. I think although it is beautiful, the location would put some people off. Still, compared to hotel solemnizations, the cost of having such a lovely outdoor venue is lower and you can use the "extra" to rent transport to the venue.
There are so many to choose from. Take your pick.
Nature also equals animal? Exotic, unique? Animal prints as well as actual animals. A definitely wow-er. You also don't have to do it outdoors per se. They also have other "indoor" venues like the Forest Lodge.
Fantastic views. I think Faber Rock is a great outdoor wedding with a view.
A beautiful sunset would be a fantastic backdrop for a wedding. In Singapore, my choice of the best beach would be in Sentosa. If you don't want the hassle of arranging for a tent etc. You can also choose to have it on the beach at any of the hotels in Sentosa. Rasa Sentosa seems to be a popular venue for beach weddings.
There are of course, many other venues such as public beaches, marinas/yacht clubs, chalets (my opinion on this would be ew but it is a cheap option and if you are good at decorating, it might be a good idea), at home in your own garden (if you are lucky enough to have a large garden), hotel poolsides... Outdoor venues are only limited by your imagination. A friend of mine (not in Singapore) got married in a public park and it was beautiful. There were people who were at the park who just joined in the celebration - one even provided impromptu music for the bridal march. Lovely!