With regards to vegetables - virtually ALL of them can last outside of the fridge. The question is: for how long? All root vegetables keep fantastically, cool dark areas are best, but even a fruit bowl with added root veggies is great. Traditional methods to store root vegetables through the winter abound, one I like is storing them in boxes in cool, clean sand. But we're just talking about a few weeks or more here, so you should be fine just keeping them out. Yes, perhaps covering them with a towel would protect them. I just keep mine in my no-longer-plugged-in fridge.
Suggestions for buying lettuce. BUY LOCAL. There is way more of a chance that it will be fresh and last longer. BUY ORGANIC - it's safer for your health. Even in the winter it is possible to find local greens at places like THE CULINARIUM if you are in Toronto and other markets. There are also local organic lettuce heads served with the roots and a bit of soil still there. These do amazingly well sans fridge. Just place the bulb of roots in a cup of water.
Greens and herbs - just put them in fresh water in cups. They look beautiful and will last for a few days. Experiment with this as some will last longer than others. For instance, Basil is a fast wilter, but also dries quite easily if just hung and turned upside down. My dandelion greens tonight look hearty and I suspect they will last me at least until 2 days from now. But the encouragement here is to eat your greens fresh!! Get that basil right on your pasta!! No time to waste. In the end, you will find that you are eating much fresher food as a result.
Almond milk, so glad you asked! Almond milk, of all the milks out there, is the absolute best for going without a fridge. It will keep longer, especially by a cool window or sitting upright in a sink of cool water. I find I can have a big glass one evening, then add it to my cereal the next morning, and finish it off later in the day. In the winter, or any time I have access to cold, the shelf life of almond milk can really last. Next to a cold window, or in a pot of fresh snow, it can last as long as it would in a fridge if you keep it cool enough, as would all milks. I have not tried. If you think you could not consume this much almond milk in the time I've mentioned, try this recipe for a fast, fresh, daily dose:
handful of almonds(preferably soaked overnight but if you forget, just go for it...use them anyway)
tiny pixie dust of salt
(below 3 ingredients optional)
dash of vanilla
sprinkle of cinnamon
drop of maple syrup, fair trade sugar, agave, or local honey.
This is by far the most fun way to consume almond milk. Takes the amount of time grabbing and tossing some almonds and rinsing the blender takes... so 1 min or so.
For a local option, try homemade oat milk:
Fill a large jug with one-third oats and two-thirds water. Mix, and leave overnight. The next morning, sieve the mixture and you will be left with a milky liquid that can be drunk as it is or used in place of cow's milk in some recipes. You can add sweeteners or other things suggested above for more flavour.
Here's an interesting article from the Guardian on 7 alternatives to milk:
Of course, winter is an amazing time to store animal milks, like goat or cow. Goat is lighter on the planet! I also feel compelled to mention as a side note that goats jump when they play, make friends with dogs and horses, climb trees, check out these photos before we move on to sauces!
goats play by jumping completely into the air...
okay, this little guy was just cute...
Find kind dairy farmers who care for their animals if they milk them!!
And animals are always best as friends!!
So many can be kept outside of the fridge after opening. I recommend still keeping them in a cool dry place if you think they will be around for a while. But any way, they will keep. All nut butters, including tahini do just find outside of the fridge. As well as non-dairy curry pastes, soy sauce, hot sauces, and beyond. Even miso will keep but is much more delicate and definitely need the cool dry place.
Hope this answers some of your questions... keep them coming!!