Hello
I'd be tempted to make little pingus out of sugarpaste and stick them on a plain white snow scene type cake (probably be easy enough to add an igloo too). You can buy black sugarpaste ready coloured (much easier but if you do decide to colour it yourself definitely use paste colouring rather than liquid). I would add up to a teaspoon (depending on quantities) of gum tragacanth to it to make it easier to work with. This 'stiffens' it (goes a bit like chewing gum). Definitely store in a cardboard box when you have made them. I expect that there are youtube type videos to make sugarpaste penguins!?!?!?
Some sponge cakes, such as madeira, you can make up to a week beforehand and I think that there are choccie cake recipes that can be made similarly in advance. You then just cover these in rolled out sugarpaste (use buttercream to stick on) and store the iced cake in a cardboard box. (Uniced in airtight, placcie box.) Cakes that can be kept are typically firmer and can be carved. You could create a slope of cake to create a bit more interest but I guess the risk is that it starts to look like a Christmas cake with too much of a snow scene!?!?!!? When exactly is it for!?!?!?
You could buy one of the stick on icing pictures from ebay and make a couple of model pingus for round the side. That could work well and you might not feel like you are cheating as much as using a stick on on its own as you obviously want to diy!!!!
Whatever you do make sure you are happy that the cake is strong enough to take it. For example, a soft victoria sponge type cake could simply collapse with too much weight of icing on it.
I take it you have googled pingu bday cake as there are loads, many of which will make you feel better about whatever you create I am sure!!!!!!
Sorry I've gone on but I say go for it.
x