Python内置函数next通过调用__next__()方法从迭代器中获取下一个元素，这样，迭代器就会向前移动到下一个元素，所以你需要多次调用next来获取头部。

[...]
    with open(output_path, 'r', encoding="utf-8") as in_f:
        cr = csv.reader(in_f, delimiter=";")
        header = next(cr)
        cw01.writerow(header)
        cw02.writerow(header)
        cw03.writerow(header)
        cw04.writerow(header)

        for line in cr:
[...]

希望能有所帮助。

当你这样做的时候会发生什么呢？我把你的代码打乱了，使它成为通用的，这样你就可以给予任何cols的列表，它会为每个col生成一个输出文件，并在csv编写器的字典中查找col。

import csv
output_path = r'C:\myfolder\large_file.csv'

def get_fhandle(col_name):
  return open(
    os.path.join(os.path.dirname(output_path), f"column1_{col_name}.csv"),
    "w", encoding="utf-8", newline=''
  )

cols = ["01", "02", "03", "04", "05"]
files = {col: get_fhandle(col) for col in cols}
try:
  writers = {
    col: csv.writer(file, delimiter=";", quoting=csv.QUOTE_MINIMAL)
    for col, file in files.items()
  }
  with open(output_path, encoding="utf-8") as in_f:
    cr = csv.reader(in_f, delimiter=";")
    header = next(cr)
    for writer in writers.values():
      writer.writerow(header)
    for line in cr:
      col = line[0][:2]
      if col not in writers:
        raise ValueError(
          f"'{col}' is not a known column. Should be: {cols.join(', ')}"
        )
      writers[col].writerow(line)
finally:
  for file in files.values():
    file.close()

使用contextlib.ExitStack()可以使事情得到实质性的清理，特别是如果我们建立一个小字典来Map输入中的哪些键Map到我们想要写入的输出文件。

import contextlib
import csv

files_out = {
    "01": "column1_01.csv",
    "02": "column1_02.csv",
    "03": "column1_03.csv",
    "04": "column1_04.csv",
}

with contextlib.ExitStack() as stack:
    ## ---------------------
    ## Set up a bunch of csv writers
    ## ---------------------
    writers = {
        key: csv.writer(stack.enter_context(open(value, "w", newline="")))
        for key, value
        in files_out.items()
    }
    ## ---------------------

    file_in = stack.enter_context(open("small.csv"))
    rows = csv.reader(file_in, delimiter=";")

    ## ---------------------
    ## write a header to each output file
    ## ---------------------
    headers = next(rows)
    for writer in writers.values():
        writer.writerow(headers)
    ## ---------------------

    ## ---------------------
    ## write rows to the appropriate file
    ## ---------------------
    for row in rows:
        key = row[0]
        if not key in writers:
            print(f"no file defined for key {key}")
            continue
        writers[key].writerow(row)
    ## ---------------------

要回答您的代码当前无法正常工作的具体问题，让我们来看一下：

with open(output_path, encoding="utf-8") as in_f:
    cr = csv.reader(in_f, delimiter=";")
    cw01.writerow(next(cr))
    cw02.writerow(next(cr))
    cw03.writerow(next(cr))
    cw04.writerow(next(cr))

    for line in cr:
        if (line[0][:2] =="01"): cw01.writerow(line)  
        if (line[0][:2] =="02"): cw02.writerow(line)  
        if (line[0][:2] =="03"): cw03.writerow(line)  
        if (line[0][:2] =="04"): cw04.writerow(line)

此处：

cw01.writerow(next(cr))

将输入文件的第一行（头）写到第一个输出文件中。然后我们重复这个过程，将连续的输入行写到输出文件中。
在将输入的前4行写入到四个输出中的每一个输出中的一行之后，我们读取输入文件中的其余行（示例中的最后两行），并根据需要将它们写入文件3和4
因此，您的具体解决方案是使用next()一次从输入文件中获取头文件，然后将其写入每个输出文件：

with open(output_path, encoding="utf-8") as in_f:
    cr = csv.reader(in_f, delimiter=";")
    headers = next(cr)

    cw01.writerow(headers)
    cw02.writerow(headers)
    cw03.writerow(headers)
    cw04.writerow(headers)

    for line in cr:
        if (line[0][:2] =="01"): cw01.writerow(line)  
        if (line[0][:2] =="02"): cw02.writerow(line)  
        if (line[0][:2] =="03"): cw03.writerow(line)  
        if (line[0][:2] =="04"): cw04.writerow(line)