If you live in a climate where winter means freezing temperatures, it’s worthwhile going through your garden shed before the cold arrives to see if there are products that must go indoors for the winter.
Obviously, hand tools can easily handle winter cold (it may be helpful to rub any metal surfaces with oil to prevent rust, whether you leave them out or not). However, if snow buildup will render your shed inaccessible for months at a time, it may be wise to move some pruning tools into the garage or the house (secateurs, pruning saw, long-handled pruning shears, etc.): they could be useful if—heaven forbid!—shrubs or trees suffer winter damage. Also, fruit trees are usually pruned in late winter, so you’ll also need those tools on hand. Power tools too (mowers, trimmers, etc.) can stay in the shed, but read the instruction manual to see if there are any specific recommendations. Freezing can, for example, to reduce the useful life of some batteries and they may need to be stored indoors.
Gloves, hats, aprons and other items of gardening clothing can theoretically overwinter in a garden shed, but then there’s a risk of rodent damage (mice, voles, etc.). The same is true for paper products. It’s best to store them indoors.
Any garden hose that contains water should be stored inside the house or a heated garage for the winter, because water expands when it freezes and could cause the hose to burst. If the hose has never been used, however, there’s no reason you couldn’t store it in the shed.
What about grass seed? When properly stored, grass seed is probably viable for at least 2 years, but if it is exposed to freezing, its germination rate may decline more quickly. It’s probably best to bring it indoors for the winter, storing it in a cool spot. Mycorrhizal fungi products also remain in better condition when stored free of frost.
Fertilizers can theoretically withstand freezing, but … liquid fertilizers will expand as they freeze and can crack their container, leading to their loss, so are safer stored indoors. You can leave dry fertilizer in the shed during the winter. Note that, over the years, dry fertilizer can cake up. This is caused by condensation and will happen both indoors and out, although condensation can be greater in a garden shed and may therefore happen more quickly. Caked fertilizer is still usable: just crumble the cake into powder before use.
With any pesticide, always read the label: if it says it should be stored cool and dry, but there is no mention of “in a frost-free place,” you can leave it in the shed. In general, dry pesticides (powders, granules, etc.) will withstand frost. However, just like dry fertilizer, can also cake up and will then be more difficult to use. Some liquid pesticides can crystallize, coagulate or come out of solution under the effect of freezing and should be stored indoors. Again, the label will tell you.
In general, any soil or soil amendment (planting soil, compost, peat moss, etc.) can remain in the shed during the winter.
Gas cans and oil containers can (and probably should) spend the winter in the garden shed or a garage rather than in the house.
What about your barbecue? Of course, you can store your barbecue in the garden shed if you want, after a thorough cleaning and oiling any surface subject to rust, but it’s much easier just to leave it outdoors under a barbecue cover. Certainly you should never store propane tanks inside any structure, be it a garden shed, a garage or a house. There is too great a risk of gas leakage, which can then accumulate inside the structure, leading to a risk of explosion. You can cover propane bottles to protect them from the elements if you want to, but leave them outdoors.
As for other products (and who knows what you have stored in your garden shed!), read the label or instruction manual: if it should be stored in a frost-free place, it will say so.