You are now settled and self-sufficient. It's time to start improving so that you can comfortably set out for adventure! You want to make sure to build an Alchemy Engine, a Lightning Rod, and a Crock Pot (in that order). The Alchemy Engine is the next step in advancing your camp. The Lightning Rod will protect your camp from Lightning Strikes which can ruin your crops and the Crockpot can produce some great foods.
After you have all this set up, depending on your resources, you may want to create a Drying Rack. If you can't comfortably kill Beefalo (or there's not enough of them to be sustainable while killing them) then you may want to set up a few Drying Racks. This will allow you to make Small Jerky from your Morsels which is a good consistent source of Health and Sanity. Do this and then use the Crock Pot to make good meals for managing Hunger.
Make sure you've crafted several chests and have a good supply of rabbit holes covered. If you have excess Logs, you can condense them into wooden boards and store twice as much wood this way. If you can find a safe nest of Spiders then use additional traps on the spiders. Set them up blocking their path to you and then lead them over the traps. This will catch and kill the spiders for you. This can allow you to drum up some more tools.
Finally, if you haven't had winter, it will start around day 21. When winter starts, you'll be able to freeze to death. A layer of ice will form around the edges of your screen. When the second layer forms, you'll start to take damage to your health and can eventually die.
Various things can keep you warm such as Wilson's beard and heavy clothing such as a Puffy Vest or Rabbit Earmuffs. Further, A Heatstone can also help keep you warm but once it loses its heat, it can actually make you freeze faster (move it to your backpack at that point since the Heatstone has no effect there). The four of those items together are the best combination to keep you warm. However, the items will not keep you warm indefinitely, they will only keep you warm longer. Eventually, you'll still start to freeze and the only way to become warmer than when you started out is to stand next to a lit campfire or fire pit. At night when you'll be by a fire anyway, unequip your warm clothing to preserve it. This way, you won't lose durability on it when you don't need it.
The cold will make it more difficult to explore but if you're properly prepared then you should be able to last for the better part of a day anyway and as long as you leave with the base parts of a fire, you should be able to make a fire quite easily/quickly should you start to Freeze. If you are not that comfortable with adventureing in the summer then you can just wait out the winter which should last for 15 days (followed by 20 days of summer).
You should continue to have the means to maintain your settlement, particularly through trapping rabbits. This should provide the food you need to survive. When you've made it through the winter, you can begin to search for the exit to the world you are in.