The ground is definitely too wet and cold to work in January. Working saturated soil can damage or destroy your soil structure. Also, avoid walking on your garden beds and planting areas which may lead to compaction of your soil.
Instead of working your garden, remove all garden debris from last season (if you have not done so already) before the cold snaps of February set it in. Good garden hygiene is essential to lessen the spread of fungal, viral, and bacterial nasties. If your garden was touched by blight, for example, remove all fallen leaves and fruit. DO NOT compost them in your home compost pile but commercial composting is fine. Once your garden is all tidied up, you can spend your time on other January tasks. Your garden will sleep until you are ready to start cultivating.
While you might not be in your garden, there are still garden tasks to be done.
1. It is a good idea to sort your seeds this month. Take stock of your inventory. Not all seeds are viable after the previous season. Onion seeds have short longevity of only 1 year, you'll need to buy new seeds every year. Label your seeds so you're aware of what you have and what you want to try next season. If you took notes of delicious or productive plants, you may want to purchase more of the same seeds.
2. Get those tools out of the rain and tend to them. Some of your tools might have stayed out in the elements this season. January is a great time to sharpen tools, oil them, and store them properly.
3. Winter is also the perfect time to plan your garden for next season. A garden journal is a great way to keep track of what you planted last season and where. For the upcoming season, consider rotating your crops as a way to keep diseases at bay.
January may seem bleak at the garden but there are many tasks that can help you start your season off with a bang. Once the garden is cleaned up, tools are cleaned and prepped, seeds inventoried and ordered, they only thing left to do is wait for spring.