c++ Faliure on vector at runtime: vector subscript out of range

consider the first line that tries to modify the data in v:

cin >> v[i].name;

This is occurring while v is an empty vector (has a size of 0). To add elements to the end of a vector you need to use push_back:

string name;
cin >> name;
v.push_back(name);

the square brackets ("[]") are for accessing an element that already exists in the vector.

In read_data you access the std::vector<Things> (Forest) v out of bounds (out of range) since the vector is empty.

You could resize it after having asked the user for how many elements that should be entered.

Example:

void read_data(Forest& v) {
    int n;

    if(std::cin >> n && n > 0) v.resize(n);   // resize

    for (int i = 0; i < v.size(); ++i) {      // use v.size() here
        std::cout << "DINTRE\n";
        std::cin >> v[i].name;
        std::cout << v[i].name << '\n';
    }
}

or simpler by using a range-based for loop:

void read_data(Forest& v) {
    int n;

    if(std::cin >> n && n > 0) v.resize(n);

    for(auto& thing : v) {
        std::cout << "DINTRE\n";
        std::cin >> thing.name;
        std::cout << thing.name << '\n';
    }
}