For icicles I have two tricks using 5 minute epoxy glue, I'm sure there are a bunch of other methods as well. Around minute four it starts getting stringy, you can anchor a glob on a toothpick and pull it down with another toothpick. If it's not quite set enough it won't hold the icicle shape, but you can wait a few seconds and try again. Generally you only have enough time to get 2-3 started before the glue is set too much. You can keep pulling at them a bit, and pushing the ends back into place if they start to curl up.
The second method is to take a strip of clear plastic, like blister pack, and cut it into narrow icicle cores with nail scissors. Then coat the cores with the epoxy glue and let it set. Be sure to get the glue all the way around each core. If you just do the front and back the epoxy can split off when you cut off the icicles to glue them in place. (I do that with CA glue.)
For ice, if you need to have something embedded in it, I think you need to do what freak describes and use a hard, clear resin like what people use for water bases. My experiments using Future and Woodland Scenics Realistic Water have been failures. They'll work for puddles, but they shrink too much for deep water. I did this one with Future and it looks okay in the picture, but a few weeks later and it was just a glossy film over the surface of the objects at the bottom of the pool.
http://www.coolminiornot.com/173704
For a more recent experiment, I did use a sheet of plastic, but this method will only work for a flat ice sheet. I got this from an Osprey terrain book. Here's the piece I used it on.
http://wyrd-games.net/photopost/showphoto.php?photo=3138
Step 1: A piece of plastic. The book writer used a sheet of plexiglass. I used a piece of clear styrene/plasticard from Evergreen (or Plastruct, can’t remember.) You could experiment with blister pack. The old blisters I had were too marked up and a little too flimsy. Cut it to fit the area you want, planning to put some sort of terrain around the edges. (I left one edge open, so you can sort of see the effect from the side.)
Step 2: Light a white or cream candle and drip blobs of wax all over the underside of the plastic.
Step 3: Heat an iron on a light setting. Put an old towel or parchment paper on your ironing surface. Put the plastic wax side down on that. Put a piece of parchment paper on top of it. Run the iron over top a few times. If the iron is too hot the wax will just melt everywhere. If it’s not quite hot enough or you’re being conservative, you might have to pass the iron over a few times. Wax might run out the edges and on to the top surface of the plastic, you should be able to gently scrape it off later. Don’t forget or go too small with the paper and/or towel to protect your ironing surface and iron, or you will get wax on them!
Step 4: If you want some cracks in the ice, gently bend the plastic a little once the wax has set.
Step 5: Paint the surface you’re going to put the ice on black or a similar dark colour. Once it’s dry, glue the ice in place with glue along the edges that will be covered by the terrain. At this point the book writer sprayed the surface with a glass etching craft spray. I didn’t have any and I liked the look of what I had as-is, so I didn’t do this part.
Step 6: Attach the terrain around the edges. I used CA to glue down my usual gravel mix for dirt bases. Then painted it and added the snow to the entire scene.
Step 7: Frosty edges. The book author used microbead snow around the edges of his pond. I used the same technique I used on the first miniature I linked. I took Reaper Master Series Anti-Shine Additive and stippled it around the edges. (I haven’t tried, but other brands of additives intended to dull down paints might work the same.) At first it doesn’t look like much, but it frosts up as it dries. It can show brush and tool marks, so if it looks too streaky, daub it with a damp sponge and let it dry and see how it looks again.