This scenario's difficulty comes from the rough terrain, but is not extraordinarily hard for experienced players.
The first step is to close down the Chairlift. Once you've expanded the park and built a path down from the second station, you can reopen the Chairlift to take some of your guests' spare change, though you can also choose to demolish it if you don't plan to build any other rides at the top of the mountain.
Having the objective of reaching a certain income of ride tickets, you should focus primarily on the rides. To make money come more quickly, build a few small roller coasters. Since it is fairly rainy, try to build rides with roofs and shelter from the rain. It may help to construct the rides inside the mountains (or with tunnels), which takes less space, increases the excitement, and will prevent people from saying "I'm not going on ___ while it's raining" since the ride is enclosed. Keeping the queue lines constant is very important to have customers paying every time. Remember that this scenario is very rainy when constructing rides. Gentle rides such as the Crooked House, which are indoors, will attract plenty of guests in the rain.
Like every park, shops and stalls are necessary, so don't forget plenty of food and drinks, (variety is key, or else you will get the "Worst Park Food" award) along with bathrooms and an Information Kiosk. Keep expanding the park and hire staff according to your need. Patrol areas are also recommended in areas with especially rough terrain.