What WW2 film am I thinking of

Hello good people of the forum!

So I’ve been trying to remember the name of a WW2 movie I saw when I was younger, I’ve done quite a bit of internet searching and tried many of the usual tactics but this is the first time I’m asking a forum…

Here’s everything I can remember about it well enough to describe.

Set during the Second World War, in winter – lots of white snowy scenes.
The movie follows a small isolated group of American soldiers, they end up in an uneasy truce with a small group of nearby German soldiers…
I recall a scene where the Germans show good intentions when they throw over one of those potato masher style grenades the Germans used, except it was a joke grenade made from a stick with a ball of snow stuck on it.

I can’t remember the exact circumstances but I think the film ends with the last few surviving Americans escaping down a mountain pass disguised as Red Cross/Medical personnel by using blood to paint the Red Cross on their uniforms, and I think also a white sheet…. I’m not sure but I think two are carrying their dead or dying comrade….

I have no idea when this film was made or even how old I was when I saw it, but I can tell you I watched it in a house I stopped living in in 2003 and it was filmed in colour (probably)

I appreciate I’m not giving much to go on, but If this fires your synapses throw me a reply.
Many thanks in advance.