Pandas - Handling NaNs in categorical data

UPDATE:

Is there a way to convert the data back to its original form after interpolation ie instead of 1,2 or 3 you have cloudy,windy and rainy again?

Solution: I've intentionally added more rows to your original DF:

In [129]: df
Out[129]:
   col1    col2
0     5  cloudy
1     3   windy
2     6     NaN
3     7   rainy
4    10     NaN
5     5  cloudy
6    10     NaN
7     7   rainy

In [130]: df.dtypes
Out[130]:
col1       int64
col2    category
dtype: object

In [131]: df.col2 = (df.col2.cat.codes.replace(-1, np.nan)
     ...:              .interpolate().astype(int).astype('category')
     ...:              .cat.rename_categories(df.col2.cat.categories))
     ...:

In [132]: df
Out[132]:
   col1    col2
0     5  cloudy
1     3   windy
2     6   rainy
3     7   rainy
4    10  cloudy
5     5  cloudy
6    10  cloudy
7     7   rainy

OLD "numerical" answer:

IIUC you can do this:

In [66]: df
Out[66]:
   col1    col2
0     5  cloudy
1     3   windy
2     6     NaN
3     7   rainy
4    10     NaN

first let's factorize col2:

In [67]: df.col2 = pd.factorize(df.col2, na_sentinel=-2)[0] + 1

In [68]: df
Out[68]:
   col1  col2
0     5     1
1     3     2
2     6    -1
3     7     3
4    10    -1

now we can interpolate it (replacing -1's with NaN's):

In [69]: df.col2.replace(-1, np.nan).interpolate().astype(int)
Out[69]:
0    1
1    2
2    2
3    3
4    3
Name: col2, dtype: int32

the same approach, but converting interpolated series to category dtype:

In [70]: df.col2.replace(-1, np.nan).interpolate().astype(int).astype('category')
Out[70]:
0    1
1    2
2    2
3    3
4    3
Name: col2, dtype: category
Categories (3, int64): [1, 2, 3]

I know your asking for linear interpolation but this is just another way if you want to do this easier.As converting categories to Numbers isn't such a good idea I suggest this one.

you can simply use the interpolation method in pandas library with method 'pad' like:

df.interpolate(method='pad')

you can also see other methods and example of using them in here. (link is the pandas documentation of interpolation)