BUG: Weighted rolling aggregations do not respect min_periods=0

[Savlik]

Pandas version checks

• I have checked that this issue has not already been reported.

• I have confirmed this bug exists on the latest version of pandas.

• I have confirmed this bug exists on the main branch of pandas.

Reproducible Example

import pandas as pd
import numpy as np

df = pd.DataFrame([np.nan, 0, 1, 2,])

print(df.rolling(window=3, win_type="exponential", min_periods=0).sum(tau=1))
#           0
# 0       NaN
# 1       NaN
# 2       NaN
# 3  1.735759
print(df.rolling(window=3, min_periods=0).sum())
#      0
# 0  0.0
# 1  0.0
# 2  1.0
# 3  3.0
print(df.rolling(window=3, win_type="exponential", min_periods=0).mean(tau=1))
#      0
# 0  NaN
# 1  NaN
# 2  NaN
# 3  1.0
print(df.rolling(window=3, min_periods=0).mean())
#      0
# 0  NaN
# 1  0.0
# 2  0.5
# 3  1.0

Issue Description

When using weighted rolling aggregation and setting min_periods to 0 does not work and it is treated as None. Aggregations without weight work as expected.

Expected Behavior

Weighted and not-weighted rolling aggregations should behave the same way with min_periods=0 and fill NaN in the same positions.

Installed Versions

commit : 2e218d1
python : 3.11.1.final.0
python-bits : 64
OS : Linux
OS-release : 5.10.102.1-microsoft-standard-WSL2
Version : #1 SMP Wed Mar 2 00:30:59 UTC 2022
machine : x86_64
processor : x86_64
byteorder : little
LC_ALL : None
LANG : C.UTF-8
LOCALE : en_US.UTF-8

pandas : 1.5.3
numpy : 1.24.1
pytz : 2022.7.1
dateutil : 2.8.2
setuptools : 66.1.1
pip : 22.2.2
Cython : None
pytest : 7.2.1
hypothesis : None
sphinx : None
blosc : None
feather : None
xlsxwriter : None
lxml.etree : None
html5lib : None
pymysql : None
psycopg2 : None
jinja2 : 3.1.2
IPython : 8.8.0
pandas_datareader: None
bs4 : 4.11.1
bottleneck : None
brotli : None
fastparquet : None
fsspec : None
gcsfs : None
matplotlib : 3.6.3
numba : None
numexpr : None
odfpy : None
openpyxl : None
pandas_gbq : None
pyarrow : 10.0.1
pyreadstat : None
pyxlsb : None
s3fs : None
scipy : 1.10.0
snappy : None
sqlalchemy : None
tables : None
tabulate : None
xarray : None
xlrd : None
xlwt : None
zstandard : None
tzdata : None

[Savlik]

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